http://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Wang&feedformat=atomUW-Math Wiki - User contributions [en]2019-08-24T14:16:02ZUser contributionsMediaWiki 1.30.1http://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17265Algebra and Algebraic Geometry Seminar Spring 20192019-04-01T17:26:46Z<p>Wang: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|Symbolic Powers in Rings of Positive Characteristic<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8 (B135)<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|Zamolodchikov periodicity and integrability<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown (Wisconsin)<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|Chow rings of matroids, ring of matroid quotients, and beyond<br />
|Daniel<br />
|-<br />
|March 8<br />
|[http://homepages.math.uic.edu/~kopper/ Jay Kopper (UIC)]<br />
|Stable restrictions of vector bundles on projective varieties<br />
|Daniel<br />
|-<br />
|March 15<br />
|[http://www.math.wisc.edu/~maxim/Sing19program.html Singularities]<br />
|No regular meeting<br />
|Max<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5 (at 11:00 in B329)<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|Log canonical thresholds, Kahler seminorms, and normalized volume<br />
|Michael<br />
|-<br />
|April 5<br />
|[http://www.math.tamu.edu/~ola/ Alexsandra Sobieska (Texas A&amp;M)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 12<br />
|Botong Wang<br />
|Lyubeznik numbers of irreducible projective varieties<br />
|local<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Daniel Smolkin===<br />
'''Symbolic Powers in Rings of Positive Characteristic'''<br />
<br />
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.<br />
<br />
===Pavlo Pylyavskyy===<br />
<br />
'''Zamolodchikov periodicity and integrability'''<br />
<br />
T-systems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic T-systems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify T-systems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin. <br />
<br />
===Michael Brown===<br />
<br />
'''Chern-Weil theory for matrix factorizations'''<br />
<br />
This is joint work with Mark Walker. Classical algebraic Chern-Weil theory provides a formula for the Chern character of a projective module P over a commutative ring in terms of a connection on P. In this talk, I will discuss an analogous formula for the Chern character of a matrix factorization. Along the way, I will provide background on matrix factorizations, and also on classical Chern-Weil theory.<br />
<br />
===Chris Eur===<br />
'''Chow rings of matroids, ring of matroid quotients, and beyond'''<br />
<br />
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.<br />
<br />
===Jay Kopper===<br />
'''Stable restrictions of vector bundles on projective varieties'''<br />
<br />
Stable vector bundles---and more generally, stable sheaves---play a role in the classification of algebraic vector bundles analogous to that of simple groups in group theory. Recent developments in this subject have extended the notion of stability to the entire derived category of sheaves. This broader perspective can be used to study the classical moduli space. In this talk I will discuss these ideas in the context of restriction theorems: situations in which a stable vector bundle remains stable when restricted to a subvariety. I will conclude with some applications to higher-rank Brill-Noether theory. This is joint work with S. Feyzbakhsh.<br />
<br />
===Shamgar Gurevich===<br />
<br />
'''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}: <br />
<br />
$$<br />
trace(\rho(g))/dim(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
===Eric Canton===<br />
'''Log canonical thresholds, Kahler seminorms, and normalized volume'''<br />
<br />
The log canonical threshold of a closed subscheme Y of an algebraic variety X gives some real number that measures the singularities of Y. This is, in turn, defined in terms of the "amount" of a given divisor that must be inserted to make X\Y a smooth variety relatively compact (i.e. proper) over X; this "amount" goes by the name of the log discrepancy of that divisor on Y. Already, the study of log discrepancies is subtle when X is a complex variety, but without the guarantee of a smooth compactification in positive characteristics, effective results can seem remote. In this talk, I present an approach to effective results in positive characteristics from my thesis. This approach is described in terms of the Berkovich analytic space associated to X, realizing the log discrepancy as a natural seminorm to put on the sheaf of Kahler differentials of X, when X is normal. I'll finish by discussing new directions related to K-stability.<br />
<br />
===Botong Wang===<br />
<br />
'''Lyubeznik numbers of irreducible projective varieties'''<br />
<br />
Lyubeznik numbers are invariants of singularities that are defined algebraically, but has topological interpretations. In positive characteristics, it is a theorem of Wenliang Zhang that the Lyubeznik numbers of the cone of a projective variety do not depend on the choice of the projective embedding. Recently, Thomas Reichelt, Morihiko Saito and Uli Walther constructed examples of reducible complex projective varieties whose Lyubeznik numbers depend on the choice of projective embeddings. I will discuss their works and a generalization to irreducible projective varieties.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17264Algebra and Algebraic Geometry Seminar Spring 20192019-04-01T17:26:22Z<p>Wang: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|Symbolic Powers in Rings of Positive Characteristic<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8 (B135)<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|Zamolodchikov periodicity and integrability<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown (Wisconsin)<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|Chow rings of matroids, ring of matroid quotients, and beyond<br />
|Daniel<br />
|-<br />
|March 8<br />
|[http://homepages.math.uic.edu/~kopper/ Jay Kopper (UIC)]<br />
|Stable restrictions of vector bundles on projective varieties<br />
|Daniel<br />
|-<br />
|March 15<br />
|[http://www.math.wisc.edu/~maxim/Sing19program.html Singularities]<br />
|No regular meeting<br />
|Max<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5 (at 11:00 in B329)<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|Log canonical thresholds, Kahler seminorms, and normalized volume<br />
|Michael<br />
|-<br />
|April 5<br />
|[http://www.math.tamu.edu/~ola/ Alexsandra Sobieska (Texas A&amp;M)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 12<br />
|Botong Wang<br />
|Lyubeznik numbers of irreducible projective varieties<br />
|local<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Daniel Smolkin===<br />
'''Symbolic Powers in Rings of Positive Characteristic'''<br />
<br />
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.<br />
<br />
===Pavlo Pylyavskyy===<br />
<br />
'''Zamolodchikov periodicity and integrability'''<br />
<br />
T-systems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic T-systems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify T-systems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin. <br />
<br />
===Michael Brown===<br />
<br />
'''Chern-Weil theory for matrix factorizations'''<br />
<br />
This is joint work with Mark Walker. Classical algebraic Chern-Weil theory provides a formula for the Chern character of a projective module P over a commutative ring in terms of a connection on P. In this talk, I will discuss an analogous formula for the Chern character of a matrix factorization. Along the way, I will provide background on matrix factorizations, and also on classical Chern-Weil theory.<br />
<br />
<br />
===Chris Eur===<br />
'''Chow rings of matroids, ring of matroid quotients, and beyond'''<br />
<br />
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.<br />
<br />
===Jay Kopper===<br />
'''Stable restrictions of vector bundles on projective varieties'''<br />
<br />
Stable vector bundles---and more generally, stable sheaves---play a role in the classification of algebraic vector bundles analogous to that of simple groups in group theory. Recent developments in this subject have extended the notion of stability to the entire derived category of sheaves. This broader perspective can be used to study the classical moduli space. In this talk I will discuss these ideas in the context of restriction theorems: situations in which a stable vector bundle remains stable when restricted to a subvariety. I will conclude with some applications to higher-rank Brill-Noether theory. This is joint work with S. Feyzbakhsh.<br />
<br />
===Shamgar Gurevich===<br />
<br />
'''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}: <br />
<br />
$$<br />
trace(\rho(g))/dim(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
<br />
===Eric Canton===<br />
'''Log canonical thresholds, Kahler seminorms, and normalized volume'''<br />
<br />
The log canonical threshold of a closed subscheme Y of an algebraic variety X gives some real number that measures the singularities of Y. This is, in turn, defined in terms of the "amount" of a given divisor that must be inserted to make X\Y a smooth variety relatively compact (i.e. proper) over X; this "amount" goes by the name of the log discrepancy of that divisor on Y. Already, the study of log discrepancies is subtle when X is a complex variety, but without the guarantee of a smooth compactification in positive characteristics, effective results can seem remote. In this talk, I present an approach to effective results in positive characteristics from my thesis. This approach is described in terms of the Berkovich analytic space associated to X, realizing the log discrepancy as a natural seminorm to put on the sheaf of Kahler differentials of X, when X is normal. I'll finish by discussing new directions related to K-stability.<br />
<br />
<br />
===Botong Wang===<br />
<br />
'''Lyubeznik numbers of irreducible projective varieties'''<br />
<br />
Lyubeznik numbers are invariants of singularities that are defined algebraically, but has topological interpretations. In positive characteristics, it is a theorem of Wenliang Zhang that the Lyubeznik numbers of the cone of a projective variety do not depend on the choice of the projective embedding. Recently, Thomas Reichelt, Morihiko Saito and Uli Walther constructed examples of reducible complex projective varieties whose Lyubeznik numbers depend on the choice of projective embeddings. I will discuss their works and a generalization to irreducible projective varieties.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17263Algebra and Algebraic Geometry Seminar Spring 20192019-04-01T17:25:41Z<p>Wang: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|Symbolic Powers in Rings of Positive Characteristic<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8 (B135)<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|Zamolodchikov periodicity and integrability<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown (Wisconsin)<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|Chow rings of matroids, ring of matroid quotients, and beyond<br />
|Daniel<br />
|-<br />
|March 8<br />
|[http://homepages.math.uic.edu/~kopper/ Jay Kopper (UIC)]<br />
|Stable restrictions of vector bundles on projective varieties<br />
|Daniel<br />
|-<br />
|March 15<br />
|[http://www.math.wisc.edu/~maxim/Sing19program.html Singularities]<br />
|No regular meeting<br />
|Max<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5 (at 11:00 in B329)<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|Log canonical thresholds, Kahler seminorms, and normalized volume<br />
|Michael<br />
|-<br />
|April 5<br />
|[http://www.math.tamu.edu/~ola/ Alexsandra Sobieska (Texas A&amp;M)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 12<br />
|Botong Wang<br />
|Lyubeznik numbers of irreducible projective varieties<br />
|local<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Daniel Smolkin===<br />
'''Symbolic Powers in Rings of Positive Characteristic'''<br />
<br />
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.<br />
<br />
===Pavlo Pylyavskyy===<br />
<br />
'''Zamolodchikov periodicity and integrability'''<br />
<br />
T-systems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic T-systems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify T-systems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin. <br />
<br />
===Michael Brown===<br />
<br />
'''Chern-Weil theory for matrix factorizations'''<br />
<br />
This is joint work with Mark Walker. Classical algebraic Chern-Weil theory provides a formula for the Chern character of a projective module P over a commutative ring in terms of a connection on P. In this talk, I will discuss an analogous formula for the Chern character of a matrix factorization. Along the way, I will provide background on matrix factorizations, and also on classical Chern-Weil theory.<br />
<br />
<br />
===Chris Eur===<br />
'''Chow rings of matroids, ring of matroid quotients, and beyond'''<br />
<br />
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.<br />
<br />
===Jay Kopper===<br />
'''Stable restrictions of vector bundles on projective varieties'''<br />
<br />
Stable vector bundles---and more generally, stable sheaves---play a role in the classification of algebraic vector bundles analogous to that of simple groups in group theory. Recent developments in this subject have extended the notion of stability to the entire derived category of sheaves. This broader perspective can be used to study the classical moduli space. In this talk I will discuss these ideas in the context of restriction theorems: situations in which a stable vector bundle remains stable when restricted to a subvariety. I will conclude with some applications to higher-rank Brill-Noether theory. This is joint work with S. Feyzbakhsh.<br />
<br />
===Shamgar Gurevich===<br />
<br />
'''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}: <br />
<br />
$$<br />
trace(\rho(g))/dim(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
===Botong Wang===<br />
<br />
'''Lyubeznik numbers of irreducible projective varieties'''<br />
<br />
Lyubeznik numbers are invariants of singularities that are defined algebraically, but has topological interpretations. In positive characteristics, it is a theorem of Wenliang Zhang that the Lyubeznik numbers of the cone of a projective variety do not depend on the choice of the projective embedding. Recently, Thomas Reichelt, Morihiko Saito and Uli Walther constructed examples of reducible complex projective varieties whose Lyubeznik numbers depend on the choice of projective embeddings. I will discuss their works and a generalization to irreducible projective varieties. <br />
<br />
===Eric Canton===<br />
'''Log canonical thresholds, Kahler seminorms, and normalized volume'''<br />
<br />
The log canonical threshold of a closed subscheme Y of an algebraic variety X gives some real number that measures the singularities of Y. This is, in turn, defined in terms of the "amount" of a given divisor that must be inserted to make X\Y a smooth variety relatively compact (i.e. proper) over X; this "amount" goes by the name of the log discrepancy of that divisor on Y. Already, the study of log discrepancies is subtle when X is a complex variety, but without the guarantee of a smooth compactification in positive characteristics, effective results can seem remote. In this talk, I present an approach to effective results in positive characteristics from my thesis. This approach is described in terms of the Berkovich analytic space associated to X, realizing the log discrepancy as a natural seminorm to put on the sheaf of Kahler differentials of X, when X is normal. I'll finish by discussing new directions related to K-stability.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17251Algebra and Algebraic Geometry Seminar Spring 20192019-04-01T15:25:11Z<p>Wang: /* Spring 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Fall 2018 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Fall 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
<br />
== Spring 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|January 25<br />
|[http://www.math.utah.edu/~smolkin/ Daniel Smolkin (Utah)]<br />
|Symbolic Powers in Rings of Positive Characteristic<br />
|Daniel<br />
|-<br />
|February 1<br />
|Juliette Bruce<br />
|Asymptotic Syzgies for Products of Projective Spaces<br />
|Local<br />
|-<br />
|February 8 (B135)<br />
|[http://www.mit.edu/~ivogt/ Isabel Vogt (MIT)]<br />
| Low degree points on curves<br />
|Wanlin and Juliette<br />
|-<br />
|February 15<br />
|Pavlo Pylyavskyy (U. Minn)<br />
|Zamolodchikov periodicity and integrability<br />
|Paul Terwilliger<br />
|-<br />
|February 22<br />
|Michael Brown (Wisconsin)<br />
|Chern-Weil theory for matrix factorizations<br />
|Local<br />
|-<br />
|March 1<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|Chow rings of matroids, ring of matroid quotients, and beyond<br />
|Daniel<br />
|-<br />
|March 8<br />
|[http://homepages.math.uic.edu/~kopper/ Jay Kopper (UIC)]<br />
|Stable restrictions of vector bundles on projective varieties<br />
|Daniel<br />
|-<br />
|March 15<br />
|[http://www.math.wisc.edu/~maxim/Sing19program.html Singularities]<br />
|No regular meeting<br />
|Max<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5 (at 11:00 in B329)<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|Log canonical thresholds, Kahler seminorms, and normalized volume<br />
|Michael<br />
|-<br />
|April 5<br />
|[http://www.math.tamu.edu/~ola/ Alexsandra Sobieska (Texas A&amp;M)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 12<br />
|Botong Wang<br />
|Lyubeznik numbers of irreducible projective varieties<br />
|local<br />
|-<br />
|April 19<br />
|[http://www-personal.umich.edu/~grifo/ Elo&iacute;sa Grifo (Michigan)]<br />
|TBD<br />
|TBD<br />
|-<br />
|April 26<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|May 3<br />
|TBD<br />
|TBD<br />
|TBD<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Daniel Smolkin===<br />
'''Symbolic Powers in Rings of Positive Characteristic'''<br />
<br />
The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!<br />
<br />
===Juliette Bruce===<br />
<br />
'''Title: Asymptotic Syzygies for Products of Projective Spaces'''<br />
<br />
I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.<br />
<br />
===Isabel Vogt===<br />
<br />
'''Title: Low degree points on curves'''<br />
<br />
In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.<br />
<br />
===Pavlo Pylyavskyy===<br />
<br />
'''Zamolodchikov periodicity and integrability'''<br />
<br />
T-systems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic T-systems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify T-systems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin. <br />
<br />
===Michael Brown===<br />
<br />
'''Chern-Weil theory for matrix factorizations'''<br />
<br />
This is joint work with Mark Walker. Classical algebraic Chern-Weil theory provides a formula for the Chern character of a projective module P over a commutative ring in terms of a connection on P. In this talk, I will discuss an analogous formula for the Chern character of a matrix factorization. Along the way, I will provide background on matrix factorizations, and also on classical Chern-Weil theory.<br />
<br />
<br />
===Chris Eur===<br />
'''Chow rings of matroids, ring of matroid quotients, and beyond'''<br />
<br />
We introduce a certain nef generating set for the Chow ring of the wonderful compactification of a hyperplane arrangement complement. This presentation yields a monomial basis of the Chow ring that admits a geometric and combinatorial interpretation with several applications. Geometrically, one can recover Poincare duality, compute the volume polynomial, and identify a portion of a polyhedral boundary of the nef cone. Combinatorially, one can generalize Postnikov's result on volumes of generalized permutohedra, prove Mason's conjecture on log-concavity of independent sets for certain matroids, and define a new valuative invariant of a matroid that measures its closeness to uniform matroids. This is an on-going joint work with Connor Simpson and Spencer Backman.<br />
<br />
===Jay Kopper===<br />
'''Stable restrictions of vector bundles on projective varieties'''<br />
<br />
Stable vector bundles---and more generally, stable sheaves---play a role in the classification of algebraic vector bundles analogous to that of simple groups in group theory. Recent developments in this subject have extended the notion of stability to the entire derived category of sheaves. This broader perspective can be used to study the classical moduli space. In this talk I will discuss these ideas in the context of restriction theorems: situations in which a stable vector bundle remains stable when restricted to a subvariety. I will conclude with some applications to higher-rank Brill-Noether theory. This is joint work with S. Feyzbakhsh.<br />
<br />
===Shamgar Gurevich===<br />
<br />
'''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}: <br />
<br />
$$<br />
trace(\rho(g))/dim(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
===Eric Canton===<br />
'''Log canonical thresholds, Kahler seminorms, and normalized volume'''<br />
<br />
The log canonical threshold of a closed subscheme Y of an algebraic variety X gives some real number that measures the singularities of Y. This is, in turn, defined in terms of the "amount" of a given divisor that must be inserted to make X\Y a smooth variety relatively compact (i.e. proper) over X; this "amount" goes by the name of the log discrepancy of that divisor on Y. Already, the study of log discrepancies is subtle when X is a complex variety, but without the guarantee of a smooth compactification in positive characteristics, effective results can seem remote. In this talk, I present an approach to effective results in positive characteristics from my thesis. This approach is described in terms of the Berkovich analytic space associated to X, realizing the log discrepancy as a natural seminorm to put on the sheaf of Kahler differentials of X, when X is normal. I'll finish by discussing new directions related to K-stability.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=File:Matrix.pdf&diff=17228File:Matrix.pdf2019-03-28T15:25:09Z<p>Wang: </p>
<hr />
<div></div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=17227Putnam Club2019-03-28T15:24:38Z<p>Wang: /* Spring 2019 */</p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 6th of February in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Matrix.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=17226Putnam Club2019-03-28T15:24:07Z<p>Wang: /* Spring 2019 */</p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 6th of February in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Putnam_03-27-19.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=17225Putnam Club2019-03-28T15:22:09Z<p>Wang: /* Spring 2019 */</p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 6th of February in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex [[Media:Ordered_Sets.pdf | Ordered Sets]]<br />
* March 6th: Mihaela [[Media: Putnam.pdf | Algebra]]<br />
* March 13: Mihaela<br />
* March 27: Botong [[Media: Putnam 03/27/19.pdf | Matrices]]<br />
<br />
If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!<br />
* February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your <br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra&diff=17178Algebra2019-03-18T19:42:34Z<p>Wang: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<br />
[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers<br />
<br />
[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics<br />
<br />
[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories<br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Richard Askey <br />
John Bascom Professor, Ph.D Princeton (1961) <br />
Research: Special Functions<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
Hiroshi Gunji <br />
Professor, Ph.D. Johns Hopkins University (1962) <br />
Research: Algebraic geometry<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
Arnold Johnson <br />
Professor, Ph.D. University of Notre Dame (1965) <br />
Research: Classical Groups<br />
<br />
Lawrence Levy <br />
Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) <br />
Research: Commutative and noncommutative ring theory<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Hans Schneider <br />
J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) <br />
Research: Linear algebra and matrix theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra&diff=17177Algebra2019-03-18T19:41:58Z<p>Wang: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<br />
[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers<br />
<br />
[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry<br />
<br />
[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics<br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Richard Askey <br />
John Bascom Professor, Ph.D Princeton (1961) <br />
Research: Special Functions<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
Hiroshi Gunji <br />
Professor, Ph.D. Johns Hopkins University (1962) <br />
Research: Algebraic geometry<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
Arnold Johnson <br />
Professor, Ph.D. University of Notre Dame (1965) <br />
Research: Classical Groups<br />
<br />
Lawrence Levy <br />
Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) <br />
Research: Commutative and noncommutative ring theory<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Hans Schneider <br />
J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) <br />
Research: Linear algebra and matrix theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra&diff=17176Algebra2019-03-18T19:41:42Z<p>Wang: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<br />
[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers<br />
<br />
[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry<br />
<br />
[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
<br />
[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics<br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Richard Askey <br />
John Bascom Professor, Ph.D Princeton (1961) <br />
Research: Special Functions<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
Hiroshi Gunji <br />
Professor, Ph.D. Johns Hopkins University (1962) <br />
Research: Algebraic geometry<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
Arnold Johnson <br />
Professor, Ph.D. University of Notre Dame (1965) <br />
Research: Classical Groups<br />
<br />
Lawrence Levy <br />
Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) <br />
Research: Commutative and noncommutative ring theory<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Hans Schneider <br />
J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) <br />
Research: Linear algebra and matrix theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra&diff=17175Algebra2019-03-18T19:37:15Z<p>Wang: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<br />
[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers<br />
<br />
[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry<br />
<br />
[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories<br />
<br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Richard Askey <br />
John Bascom Professor, Ph.D Princeton (1961) <br />
Research: Special Functions<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
Hiroshi Gunji <br />
Professor, Ph.D. Johns Hopkins University (1962) <br />
Research: Algebraic geometry<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
Arnold Johnson <br />
Professor, Ph.D. University of Notre Dame (1965) <br />
Research: Classical Groups<br />
<br />
Lawrence Levy <br />
Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) <br />
Research: Commutative and noncommutative ring theory<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Hans Schneider <br />
J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) <br />
Research: Linear algebra and matrix theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=16877Putnam Club2019-02-08T16:33:43Z<p>Wang: </p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 6th of February in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam_Basics_2019.pdf | The basics]] by Botong<br />
* February 13: Botong<br />
* February 20: Alex<br />
* February 27: Alex<br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=16862Putnam Club2019-02-06T22:44:39Z<p>Wang: </p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
<br />
==Spring 2019==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 6th of February in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
* February 6: [[Media:Putnam basics 2019.pdf | Basics]]Botong<br />
* February 13: Botong<br />
* February 20: Alex<br />
* February 27: Alex<br />
* March 6th: Mihaela<br />
* March 13: Mihaela<br />
etc.<br />
<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
* November 14: [[Media:group.pdf | Techniques from Group Theory]] by Alex Hanhart.<br />
<br />
* November 21: '''No meeting''': Happy Thanksgiving!<br />
<br />
* November 28: [[Media:Putnam_November_28_2018.pdf | Number Theory]] by Mihaela Ifrim.<br />
<br />
* December 1: Putnam Competition! Starts at 9am!!!! '''The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.'''<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=16334Putnam Club2018-11-04T04:05:46Z<p>Wang: /* Fall 2018 */</p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 3: [[Media:Putnam_Oct_3_2018.pdf | Linear Algebra]] by George Craciun.<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang.<br />
<br />
* October 17: [[Media:SeqPut18.pdf | Sequences]] by Alex Hanhart.<br />
<br />
* October 24: [[Media:Putnam_Oct_24th_2018.pdf | Convergence and Continuity]] by Mihaela Ifrim.<br />
<br />
* October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.<br />
<br />
* October 31: [[Media:Putnam_Oct_31_2018.pdf | Geometry: cartesian coordinates, complex coordinates, circles and conics]] by George Craciun.<br />
<br />
* November 7: [[Media:Putnam_Combinatorics_2018.pdf | Combinatorics: Set theory and geometric combinatorics]] by Botong Wang.<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=File:Putnam_Combinatorics_2018.pdf&diff=16333File:Putnam Combinatorics 2018.pdf2018-11-04T04:03:12Z<p>Wang: </p>
<hr />
<div></div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=16287Algebra and Algebraic Geometry Seminar Fall 20182018-10-27T16:48:43Z<p>Wang: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]], [[Algebra and Algebraic Geometry Seminar Spring 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings<br />
|Local<br />
|-<br />
|September 14<br />
|Akhil Mathew (U Chicago)<br />
|Kaledin's noncommutative degeneration theorem and topological Hochschild homology<br />
|Andrei<br />
|-<br />
|September 21<br />
|Andrei Caldararu<br />
|Categorical Gromov-Witten invariants beyond genus 1<br />
|Local<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|Conjecture D for matrix factorizations<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|Modified quantum difference Toda systems<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|[https://juliettebruce.github.io Juliette Bruce]<br />
|Covering Abelian Varieties and Effective Bertini<br />
|Local<br />
|-<br />
|November 2<br />
|[http://sites.nd.edu/b-taji/ Behrouz Taji] (Notre Dame)<br />
|Remarks on the Kodaira dimension of base spaces of families of manifolds<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|[http://www-personal.umich.edu/~rohitna/ Rohit Nagpal (Michigan)]<br />
|TBD<br />
|John WG<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|December 14<br />
|TBD (this date is now open again!)<br />
|TBD<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Akhil Mathew===<br />
<br />
'''Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology'''<br />
<br />
For a smooth proper variety over a field of characteristic<br />
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology<br />
of differential forms to de Rham cohomology) is well-known to<br />
degenerate, via Hodge theory. A "noncommutative" version of this<br />
theorem has been proved by Kaledin for smooth proper dg categories<br />
over a field of characteristic zero, based on the technique of<br />
reduction mod p. I will describe a short proof of this theorem using<br />
the theory of topological Hochschild homology, which provides a<br />
canonical one-parameter deformation of Hochschild homology in<br />
characteristic p.<br />
<br />
===Andrei Caldararu===<br />
'''Categorical Gromov-Witten invariants beyond genus 1'''<br />
<br />
In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a <br />
Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical<br />
Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category<br />
is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's<br />
approach and recent progress (with Junwu Tu) on extending computations of these invariants<br />
past genus 1.<br />
<br />
===Mark Walker===<br />
'''Conjecture D for matrix factorizations'''<br />
<br />
Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.<br />
<br />
===Oleksandr Tsymbaliuk===<br />
'''Modified quantum difference Toda systems'''<br />
<br />
The q-version of a Toda system associated with any Lie algebra was introduced independently by Etingof and Sevostyanov in 1999. In this talk, we shall discuss the generalization of this construction which naturally produces a family of 3^{rk(g)-1} similar integrable systems. One of the key ingredients in the proof is played by the fermionic formula for the J-factors (defined as pairing of two Whittaker vectors in Verma modules), due to Feigin-Feigin-Jimbo-Miwa-Mukhin. In types A and C, our construction admits an alternative presentation via local Lax matrices, similar to the classical construction of Faddeev-Takhtajan for the classical type A Toda system. Finally, we shall discuss the geometric interpretation of Whittaker vectors in type A. <br />
<br />
This talk is based on the joint work with M. Finkelberg and R. Gonin.<br />
<br />
===Juliette Bruce===<br />
'''Covering Abelian Varieties and Effective Bertini'''<br />
<br />
I will discuss recent work showing that every abelian variety is covered by a Jacobian whose dimension is bounded. This is joint with Wanlin Li.<br />
<br />
===Behrouz Taji===<br />
<br />
'''Remarks on the Kodaira dimension of base spaces of families of manifolds'''<br />
<br />
A conjecture of Shafarevich and Viehweg predicted that <br />
a family of smooth projective manifolds with good minimal models<br />
have (log-)general type base spaces, if the family has maximal variation.<br />
Generalizing this problem, Kebekus and Kovács conjectured that the <br />
Kodaira dimension of base spaces of such manifolds should <br />
define an upper bound for the variation in the family, even if the variation <br />
is not maximal. My aim in this talk is to discuss a strategy to solve this problem.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=16156Putnam Club2018-10-05T15:49:27Z<p>Wang: </p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by M. Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 10: [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang. <br />
<br />
<br />
<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Putnam_Club&diff=16155Putnam Club2018-10-05T15:49:02Z<p>Wang: </p>
<hr />
<div><br />
''Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.<br />
<br />
[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]<br />
<br />
The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information [http://www.math.vt.edu/people/plinnell/Vtregional/ over here.]<br />
<br />
We also hold our own UW Madison [[Undergraduate Math Competition]] in the spring; for this academic year, it is tentatively scheduled in April 2019.<br />
<br />
==Fall 2018==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. '''The first meeting will be on the 26th of September in Van Vleck hall, room B139.'''<br />
<br />
'''! Important announcement:''' We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu. <br />
<br />
<br />
<br />
* September 26: topic [[Media:Putnam_26_sept_2018.pdf | Introductory meeting]] by M. Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!<br />
<br />
* October 10: topic [[Media:Putnam polynomials 2018.pdf | Polynomials]] by Botong Wang. <br />
<br />
<br />
<br />
<br />
==Spring 2018==<br />
<br />
The Putnam Club does not meet in the spring, but we had the fourth annual UW [[Undergraduate Math Competition]] on '''April 24th''', 2018, 5:30-8pm in VV B239.<br />
<br />
==Fall 2017==<br />
<br />
The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.<br />
<br />
* September 20: [[Media:Putnam092017.pdf | Introductory meeting]] by D.Arinkin<br />
* September 27: [[Media:Putnam092717.pdf | Equations with functions as unknowns]] by M.Ifrim (by request: here is [[Media:Putnam092717sol6.pdf | a solution to problem 6]]; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution [http://kskedlaya.org/putnam-archive/2016s.pdf here]).<br />
* October 4: [[Media:Putnam100417.pdf | Inequalities ]] by G.Craciun.<br />
* October 11: [[Media:Putnam101117.pdf | Polynomials ]] by D.Arinkin.<br />
* October 18: [[Media:Putnam1(2)..pdf | Equations ]] by M. Ifrim<br />
* October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.<br />
* October 25: Review of this year's [[Media:VTRMC2017.pdf | Virginia Tech Contest]] by G.Craciun.<br />
* November 1: [[Media:Putnam110117.pdf | Functions and calculus]] by D.Arinkin.<br />
* November 8: [[Media:Putnam1.pdf | Past Competitions]] by M.Ifrim<br />
* November 15: [[Media:Putnam111517.pdf | Recurrences]] by G.Craciun.<br />
* November 22: '''No meeting''': Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112917.pdf | Complex numbers]] by D.Arinkin.<br />
* December 2: '''Putnam Exam''' in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the third annual UW [[Undergraduate Math Competition]] on April 19th, 2017.<br />
<br />
==Fall 2016==<br />
<br />
* September 20: [[Media:Putnam092016.pdf | Introductory meeting]]<br />
* September 27: [[Media:Putnam092716.pdf | Calculus and analysis]]<br />
* October 4: [[Media:Putnam100416.pdf | Generating functions]] (by Vlad Matei) <br />
* October 11: [[Media:UWUMC2016.pdf | Review of last year's UW Math competition]]<br />
* October 18: [[Media:Putnam101816.pdf | Functional equations]]<br />
* October 22: Virginia Tech Math Contest<br />
* October 25: Review of this year's [[Media:vtrmc16.pdf | VT contest]]<br />
* November 1: [[Media:Putnam110116.pdf | Matrices]] (by Vlad Matei)<br />
* November 15: [[Media:Putnam111516.pdf | Two algebra problems]]<br />
* November 22: No meeting: Happy Thanksgiving!<br />
* November 29: [[Media:Putnam112916.pdf | Assorted problems]]<br />
* December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.<br />
<br />
==Spring 2016==<br />
<br />
The Putnam Club does not meet in the spring, but we had the second annual UW [[Undergraduate Math Competition]] on April 12th, 2016.<br />
<br />
==Fall 2015==<br />
. <br />
* September 23rd: [[Media:Putnam092315.pdf | Introductory meeting]]<br />
* September 30th: [[Media:Putnam093015.pdf | Pigeonhole principle]]<br />
* October 7th: Review of [[Media:UWUMC2015.pdf | 2015 UW math competition]]<br />
* October 14th: [[Media:Putnam101415.pdf | Matrices and determinants]]<br />
* October 21st: [[Media:Putnam102115.pdf | Virginia Tech practice]]<br />
* October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am<br />
* October 28th: Review of the 2015 Virginia Tech contest.<br />
* November 4th: [[Media:PutnamProblemsOct12.pdf | Polynomials]]<br />
* November 11th: [[Media:PutnamProblemsNov11.pdf | Assorted problems]]<br />
* November 18th: [[Media:PutnamProblemsNov18.pdf | Assorted problems]]<br />
* No meeting on November 25th<br />
* December 2nd: TBA<br />
* December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.<br />
<br />
==Spring 2015==<br />
<br />
The Putnam Club does not meet in the spring, but we had our first UW [[Undergraduate Math Competition]]!<br />
<br />
==Fall 2014==<br />
<br />
* September 17: [[Media:Putnam091714.pdf | Introductory meeting]]<br />
* September 22: [[Media:Putnam092214.pdf | Coloring and pigeonhole principle]]<br />
* October 1st: Went through HW problems from last time<br />
* October 8th: [[Media:Putnam100814.pdf | Number theory]]<br />
* October 15th: [[Media:Putnam101514.pdf | Games]]<br />
* October 22nd: [[Media:VTRMC13.pdf | Problems from last year's Virginia Tech contest]]<br />
* October 25th: Virginia Tech Regional Mathematics Contest<br />
* October 29th: Review of this year's Virginia Tech contest<br />
* November 5th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/06-inequalities.pdf Inequalities] and [http://www.math.cmu.edu/~lohp/docs/math/2014-295/05-functional.pdf functional equations]<br />
* November 12th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/02-polynomials.pdf Polynomials]<br />
* November 19th: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/10-combinatorics.pdf Combinatorics]<br />
* December 3rd: [http://www.math.cmu.edu/~lohp/docs/math/2014-295/08-recursions.pdf Recursions]<br />
* December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119<br />
* December 10th: Review of [http://www.artofproblemsolving.com/Forum/resources/files/undergraduate_competitions/Undergraduate_Competitions-Putnam-2014-23 this year's Putnam]<br />
<br />
==Fall 2013==<br />
<br />
<br />
* September 11: [[Media:Putnam091113.pdf | Introductory Meeting]]<br />
* September 18: [[Media:Putnam091813.pdf | Assorted Problems]] (by Yihe Dong) <br />
* September 25: [[Media:Putnam092513.pdf | Combinatorics]]<br />
* October 2: [[Media:Putnam100213.pdf | Matrices and Linear Algebra]]<br />
* October 9: [[Media:Putnam100913.pdf | Number Theory]]<br />
* October 16: [[Media:Putnam101613.pdf | Functions and Calculus]]<br />
* October 23: [[Media:Putnam102313.pdf | Polynomials]]<br />
* October 26: Virginia Tech Regional Mathematics Contest<br />
* October 30: [[Media:VTRMC13.pdf | Problems from this year's Virginia Tech contest]]<br />
* November 6: [[Media:Putnam110413.pdf | Games]]<br />
* November 13: [[Media:Putnam111113.pdf | Pigeonhole Principle]]<br />
* November 20: [[Media:Putnam112013.pdf | Extreme Principle]]<br />
* November 27: No meeting (Thanksgiving)<br />
* December 4: TBA<br />
* December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.<br />
<br />
==Fall 2012==<br />
<br />
* September 11: Introduction [[Media:Putnam2012IntroProblems.pdf | Problems]]<br />
* September 18: Some Basic Techniques [[Media:Putnam2012Week1Problems.pdf | Problems]]<br />
* September 25: Polynomials and Algebra [[Media:Putnam2012Week2Problems.pdf | Problems]]<br />
* October 2: Number Theory [[Media:Putnam2012Week3Problems.pdf | Problems]]<br />
* October 9: Calculus [[Media:Putnam2012Week4Problems.pdf | Problems]]<br />
* October 16: Games and Algorithms [[Media:Putnam2012Week5Problems.pdf | Problems]]<br />
* October 23: Combinatorics [[Media:Putnam2012Week6Problems.pdf | Problems]]<br />
* October 30: Probability [[Media:Putnam2012Week7Problems.pdf | Problems]]<br />
* November 6: Linear Algebra [[Media:Putnam2012Week8Problems.pdf | Problems]]<br />
* November 13: Grab Bag [[Media:Putnam2012Week9Problems.pdf | Problems]]<br />
* November 27: Grab Bag 2 [[Media:Putnam2012Week10Problems.pdf | Problems]]<br />
<br />
==Fall 2011==<br />
<br />
* September 21: Pigeonhole Principle (Brian Rice) [[Media:PutnamProblemsSept21.pdf | Problems]]<br />
* September 28: Introduction to Counting (Brian Rice) [[Media:PutnamProblemsSept28.pdf | Problems]]<br />
* October 5: Elementary Number Theory (Brian Rice) [[Media:PutnamProblemsOct5.pdf | Problems]], [[Media:PutnamProblemsOct5Hard.pdf | Problems (Hardcore)]]<br />
* October 12: Polynomials (Brian Rice) [[Media:PutnamProblemsOct12.pdf | Problems]], [[Media:PutnamProblemsOct12Hard.pdf | Problems (Hardcore)]]<br />
* October 19: A Grab Bag of Discrete Math (Brian Rice) [[Media:PutnamProblemsOct19.pdf | Problems]]<br />
* October 26: Calculus, Week 1 (Brian Rice) [[Media:PutnamProblemsOct26.pdf | Problems]]<br />
* November 2: Calculus, Week 2 (Brian Rice) [[Media:PutnamProblemsNov2.pdf | Problems]]<br />
* November 9: Linear and Abstract Algebra (Brian Rice) [[Media: PutnamProblemsNov9.pdf | Problems]]<br />
* November 16: Mock Putnam [[Media: MockPutnamProblems.pdf | Problems]], [[Media: MockPutnamSolutions.pdf | Solutions]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=File:Putnam_polynomials_2018.pdf&diff=16154File:Putnam polynomials 2018.pdf2018-10-05T15:47:11Z<p>Wang: </p>
<hr />
<div></div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=16070Algebra and Algebraic Geometry Seminar Fall 20182018-09-25T17:09:16Z<p>Wang: /* Fall 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]], [[Algebra and Algebraic Geometry Seminar Spring 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings<br />
|Local<br />
|-<br />
|September 14<br />
|Akhil Mathew (U Chicago)<br />
|Kaledin's noncommutative degeneration theorem and topological Hochschild homology<br />
|Andrei<br />
|-<br />
|September 21<br />
|Andrei Caldararu<br />
|Categorical Gromov-Witten invariants beyond genus 1<br />
|Local<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|Conjecture D for matrix factorizations<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|TBD<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|Juliette Bruce<br />
|TBD<br />
|Local<br />
|-<br />
|November 2<br />
|[http://sites.nd.edu/b-taji/ Behrouz Taji] (Notre Dame)<br />
|TBD<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|Saved<br />
|TBD<br />
|Local<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|[http://www-personal.umich.edu/~grifo/ Eloísa Grifo] (Michigan)<br />
|TBD<br />
|Daniel<br />
|-<br />
|December 7<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|December 14<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Akhil Mathew===<br />
<br />
'''Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology'''<br />
<br />
For a smooth proper variety over a field of characteristic<br />
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology<br />
of differential forms to de Rham cohomology) is well-known to<br />
degenerate, via Hodge theory. A "noncommutative" version of this<br />
theorem has been proved by Kaledin for smooth proper dg categories<br />
over a field of characteristic zero, based on the technique of<br />
reduction mod p. I will describe a short proof of this theorem using<br />
the theory of topological Hochschild homology, which provides a<br />
canonical one-parameter deformation of Hochschild homology in<br />
characteristic p.<br />
<br />
===Andrei Caldararu===<br />
'''Categorical Gromov-Witten invariants beyond genus 1'''<br />
<br />
In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a <br />
Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical<br />
Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category<br />
is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's<br />
approach and recent progress (with Junwu Tu) on extending computations of these invariants<br />
past genus 1.<br />
<br />
===Mark Walker===<br />
'''Conjecture D for matrix factorizations'''<br />
<br />
Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Geometry_and_Topology&diff=16009Geometry and Topology2018-09-18T21:08:23Z<p>Wang: </p>
<hr />
<div>=='''Seminars'''==<br />
<br />
<b><font size="3">[[Geometry and Topology Seminar]]</font></b><br />
<br />
[[PDE Geometric Analysis seminar]]<br />
<br />
[[Symplectic Geometry Seminar]]<br />
<br />
== '''Faculty''' ==<br />
<br />
'''Faculty in Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (U Chicago 2007) Geometric group theory, quasi-isometric rigidity.<br />
<br />
[http://www.math.wisc.edu/~kent Autumn Kent] (UT Austin 2006) <br />
Hyperbolic geometry, mapping class groups, geometric group theory, connections to algebra.<br />
<br />
[http://www.math.wisc.edu/~maribeff/ Gloria Mari-Beffa] (U Minnesota &ndash; Minneapolis 1991) <br />
Differential geometry, invariant theory, completely integrable systems.<br />
<br />
[http://www.math.wisc.edu/~maxim/ Laurentiu Maxim] (U Penn 2005)<br />
Geometry and topology of singularities.<br />
<br />
[http://www.math.wisc.edu/~stpaul/ Sean T. Paul] (Princeton 2000)<br />
Complex differential geometry.<br />
<br />
[http://www.math.wisc.edu/~bwang/ Bing Wang] (UW &ndash; Madison 2008) <br />
Geometric flows.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang] (Purdue 2012) <br />
Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
[http://www.sites.google.com/a/wisc.edu/lu-wang/ Lu Wang] (MIT 2011) <br />
Geometric partial differential equations.<br />
<br />
<br />
'''Faculty with research tied to Geometry and Topology'''<br />
<br />
[http://www.math.wisc.edu/~angenent/ Sigurd Angenent] (Leiden 1986) Partial differential equations.<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru] (Cornell 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (UT Austin 1998) Fluid dynamics, mixing, biological swimming and mixing, topological dynamics.<br />
<br />
<br />
'''Postdoctoral faculty in Geometry and Topology'''<br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova] (U Penn 2015)<br />
Low-dimensional topology, knot theory<br />
<br />
<br />
'''Honorary Fellow'''<br />
<br />
Morris Hirsch (U Chicago 1958)<br />
<br />
<br />
'''Emeriti'''<br />
<br />
Edward Fadell (Ohio State 1952)<br />
<br />
Sufiàn Husseini (Princeton 1960)<br />
Algebraic topology and applications.<br />
<br />
[http://www.math.wisc.edu/~robbin/ Joel Robbin] (Princeton 1965)<br />
Dynamical systems and symplectic geometry.<br />
<br />
Peter Orlik (U Michigan 1966)<br />
<br />
Mary Ellen Rudin (UT Austin 1949)<br />
<br />
=='''Conferences'''==<br />
<br />
'''Upcoming conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~rkent/MXRI.html Moduli Crossroads Retreat, I]<br />
<br />
'''Previous conferences in Geometry and Topology held at UW'''<br />
<br />
[http://www.math.wisc.edu/~dymarz/yggt/ Young Geometric Group Theory in the Midwest Workshop]<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day]<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/home Mirror Symmetry in the Midwest II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest, IV]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing16.html Singularities in the Midwest, III]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing12.html Singularities in the Midwest, II]<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest]<br />
<br />
[http://www.math.wisc.edu/~oh/glgc/ 2010 Great Lakes Geometry Conference]<br />
<br />
<br />
<!-- ''Graduate study in Geometry and Topology at UW-Madison''' --></div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra&diff=16008Algebra2018-09-18T21:07:27Z<p>Wang: </p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<br />
[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)<br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<br />
[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.<br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. <br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<br />
[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers<br />
<br />
[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry<br />
<br />
[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories<br />
<br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[http://uw-aas.tumblr.com Applied Algebra Seminar] (Thursdays 11)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Richard Askey <br />
John Bascom Professor, Ph.D Princeton (1961) <br />
Research: Special Functions<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
Hiroshi Gunji <br />
Professor, Ph.D. Johns Hopkins University (1962) <br />
Research: Algebraic geometry<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
Arnold Johnson <br />
Professor, Ph.D. University of Notre Dame (1965) <br />
Research: Classical Groups<br />
<br />
Lawrence Levy <br />
Professor, Ph.D. University of Illinois at Urbana-Champaign (1961) <br />
Research: Commutative and noncommutative ring theory<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Hans Schneider <br />
J. J. Sylvester Professor of Mathematics, Ph.D. University of Edinburgh (1952) <br />
Research: Linear algebra and matrix theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=15870Algebra and Algebraic Geometry Seminar Fall 20182018-09-05T15:42:53Z<p>Wang: /* Fall 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings and Stillman's Conjecture<br />
|Local<br />
|-<br />
|September 14<br />
|<br />
|<br />
|<br />
|-<br />
|September 21<br />
|<br />
|<br />
|<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|TBD<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|TBD<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|<br />
|<br />
|<br />
|-<br />
|November 2<br />
|Behrouz Taji (Notre Dame)<br />
|TBD<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|-TBD<br />
|-TBD<br />
|-TBD<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|December 14<br />
|-TBD<br />
|-TBD<br />
|-TBD<br />
|-<br />
|}<br />
<br />
== Abstracts ==</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=15869Algebra and Algebraic Geometry Seminar Fall 20182018-09-05T15:41:51Z<p>Wang: /* Fall 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings and Stillman's Conjecture<br />
|Local<br />
|-<br />
|September 14<br />
|<br />
|<br />
|<br />
|-<br />
|September 21<br />
|<br />
|<br />
|<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|TBD<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|TBD<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|<br />
|<br />
|<br />
|-<br />
|November 2<br />
|-Behrouz Taji (Notre Dame)<br />
|-TBD<br />
|-Botong Wang<br />
|-<br />
|November 9<br />
|-TBD<br />
|-TBD<br />
|-TBD<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|December 14<br />
|-TBD<br />
|-TBD<br />
|-TBD<br />
|-<br />
|}<br />
<br />
== Abstracts ==</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15848Colloquia/Fall182018-09-04T15:58:08Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15847Colloquia/Fall182018-09-04T15:57:30Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| Eyal Subag (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15846Colloquia/Fall182018-09-04T15:56:19Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| Eyal Subag (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15677Colloquia/Fall182018-08-06T15:31:48Z<p>Wang: /* Fall 2018 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| Eyal Subag (Penn State)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=15560Colloquia/Fall182018-06-20T01:23:47Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguish Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 12<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15445Algebra and Algebraic Geometry Seminar Spring 20182018-04-20T14:38:32Z<p>Wang: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|Stability in the homology of Deligne-Mumford compactifications]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~weiho/ Wei Ho (Michigan)]<br />
|Noncommutative Galois closures and moduli problems<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|[https://sites.google.com/site/dcorey2814/ Daniel Corey (Yale)]<br />
|[#Corey|Initial degenerations of Grassmannians]<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|Irrationality problems]]<br />
|Jordan<br />
|-<br />
|'''April 23''' 2:30-3:30 at 225 Ingraham<br />
|Nero Budur (Leuven)<br />
|[[#Nero Budur|Homotopy of singular algebraic varieties]]<br />
|Botong<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Phil Tosteson===<br />
<br />
'''Stability in the homology of Deligne-Mumford compactifications'''<br />
<br />
The space <math>\bar M_{g,n}</math> is a compactification of the moduli space algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the asymptotic behavior of its homology, <math>H_i(\bar M_{g,n})</math>, for <math>n \gg 0</math> can be studied using the representation theory of the category of finite sets and surjections.<br />
<br />
===Wei Ho===<br />
<br />
'''Noncommutative Galois closures and moduli problems'''<br />
<br />
In this talk, we will discuss the notion of a Galois closure for a possibly noncommutative algebra. We will explain how this problem is related to certain moduli problems involving genus one curves and torsors for Jacobians of higher genus curves. This is joint work with Matt Satriano.<br />
<br />
===Daniel Corey===<br />
<br />
'''Initial degenerations of Grassmannians'''<br />
<br />
Let Gr_0(d,n) denote the open subvariety of the Grassmannian Gr(d,n) consisting of d-1 dimensional subspaces of P^{n-1} meeting the toric boundary transversely. We prove that Gr_0(3,7) is schoen in the sense that all of its initial degenerations are smooth. The main technique we will use is to express the initial degenerations of Gr_0(3,7) as a inverse limit of thin Schubert cells. We use this to show that the Chow quotient of Gr(3,7) by the maximal torus H in GL(7) is the log canonical compactification of the moduli space of 7 lines in P^2 in linear general position.<br />
<br />
===Alena Pirutka===<br />
<br />
'''Irrationality problems'''<br />
<br />
Let X be a projective algebraic variety, the set of solutions of a system of homogeneous polynomial equations. Several classical notions describe how ``unconstrained'' the solutions are, i.e., how close X is to projective space: there are notions of rational, unirational and stably rational varieties. Over the field of complex numbers, these notions coincide in dimensions one and two, but diverge in higher<br />
dimensions. In the last years, many new classes of non stably rational varieties were found, using a specialization technique, introduced by C. Voisin. This method also allowed to prove that the rationality is not a deformation invariant in smooth and projective families of complex varieties: this is a joint work with B. Hassett and Y. Tschinkel. In my talk I will describe classical examples, as well as the recent progress around these rationality questions.<br />
<br />
===Nero Budur===<br />
<br />
'''Homotopy of singular algebraic varieties'''<br />
<br />
By work of Simpson, Kollár, Kapovich, every finitely generated group can be the fundamental group of an irreducible complex algebraic variety with only normal crossings and Whitney umbrellas as singularities. In contrast, we show that if a complex algebraic variety has no weight zero 1-cohomology classes, then the fundamental group is strongly restricted: the irreducible components of the cohomology jump loci of rank one local systems containing the constant sheaf are complex affine tori. Same for links and Milnor fibers. This is joint work with Marcel Rubió.<br />
<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15444Algebra and Algebraic Geometry Seminar Spring 20182018-04-20T14:37:57Z<p>Wang: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|Stability in the homology of Deligne-Mumford compactifications]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~weiho/ Wei Ho (Michigan)]<br />
|Noncommutative Galois closures and moduli problems<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|[https://sites.google.com/site/dcorey2814/ Daniel Corey (Yale)]<br />
|[#Corey|Initial degenerations of Grassmannians]<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|Irrationality problems]]<br />
|Jordan<br />
|-<br />
|'''April 23''' 2:30-3:30 at 225 Ingraham<br />
|Nero Budur (Leuven)<br />
|[[#Nero Budur|Homotopy of singular algebraic varieties]]<br />
|Botong<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Phil Tosteson===<br />
<br />
'''Stability in the homology of Deligne-Mumford compactifications'''<br />
<br />
The space <math>\bar M_{g,n}</math> is a compactification of the moduli space algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the asymptotic behavior of its homology, <math>H_i(\bar M_{g,n})</math>, for <math>n \gg 0</math> can be studied using the representation theory of the category of finite sets and surjections.<br />
<br />
===Wei Ho===<br />
<br />
'''Noncommutative Galois closures and moduli problems'''<br />
<br />
In this talk, we will discuss the notion of a Galois closure for a possibly noncommutative algebra. We will explain how this problem is related to certain moduli problems involving genus one curves and torsors for Jacobians of higher genus curves. This is joint work with Matt Satriano.<br />
<br />
===Daniel Corey===<br />
<br />
''Initial degenerations of Grassmannians''<br />
<br />
Let Gr_0(d,n) denote the open subvariety of the Grassmannian Gr(d,n) consisting of d-1 dimensional subspaces of P^{n-1} meeting the toric boundary transversely. We prove that Gr_0(3,7) is schoen in the sense that all of its initial degenerations are smooth. The main technique we will use is to express the initial degenerations of Gr_0(3,7) as a inverse limit of thin Schubert cells. We use this to show that the Chow quotient of Gr(3,7) by the maximal torus H in GL(7) is the log canonical compactification of the moduli space of 7 lines in P^2 in linear general position.<br />
<br />
===Alena Pirutka===<br />
<br />
"Irrationality problems"<br />
<br />
Let X be a projective algebraic variety, the set of solutions of a system of homogeneous polynomial equations. Several classical notions describe how ``unconstrained'' the solutions are, i.e., how close X is to projective space: there are notions of rational, unirational and stably rational varieties. Over the field of complex numbers, these notions coincide in dimensions one and two, but diverge in higher<br />
dimensions. In the last years, many new classes of non stably rational varieties were found, using a specialization technique, introduced by C. Voisin. This method also allowed to prove that the rationality is not a deformation invariant in smooth and projective families of complex varieties: this is a joint work with B. Hassett and Y. Tschinkel. In my talk I will describe classical examples, as well as the recent progress around these rationality questions.<br />
<br />
===Nero Budur===<br />
<br />
'''Homotopy of singular algebraic varieties'''<br />
<br />
By work of Simpson, Kollár, Kapovich, every finitely generated group can be the fundamental group of an irreducible complex algebraic variety with only normal crossings and Whitney umbrellas as singularities. In contrast, we show that if a complex algebraic variety has no weight zero 1-cohomology classes, then the fundamental group is strongly restricted: the irreducible components of the cohomology jump loci of rank one local systems containing the constant sheaf are complex affine tori. Same for links and Milnor fibers. This is joint work with Marcel Rubió.<br />
<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15443Algebra and Algebraic Geometry Seminar Spring 20182018-04-20T14:37:21Z<p>Wang: </p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|Stability in the homology of Deligne-Mumford compactifications]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~weiho/ Wei Ho (Michigan)]<br />
|Noncommutative Galois closures and moduli problems<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|[https://sites.google.com/site/dcorey2814/ Daniel Corey (Yale)]<br />
|[#Corey|Initial degenerations of Grassmannians]<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|Irrationality problems]]<br />
|Jordan<br />
|-<br />
|'''April 23''' 2:30-3:30 at 225 Ingraham<br />
|Nero Budur (Leuven)<br />
|[[#Nero Budur|Homotopy of singular algebraic varieties]]<br />
|Botong<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Phil Tosteson===<br />
<br />
'''Stability in the homology of Deligne-Mumford compactifications'''<br />
<br />
The space <math>\bar M_{g,n}</math> is a compactification of the moduli space algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the asymptotic behavior of its homology, <math>H_i(\bar M_{g,n})</math>, for <math>n \gg 0</math> can be studied using the representation theory of the category of finite sets and surjections.<br />
<br />
===Wei Ho===<br />
<br />
'''Noncommutative Galois closures and moduli problems'''<br />
<br />
In this talk, we will discuss the notion of a Galois closure for a possibly noncommutative algebra. We will explain how this problem is related to certain moduli problems involving genus one curves and torsors for Jacobians of higher genus curves. This is joint work with Matt Satriano.<br />
<br />
===Daniel Corey===<br />
<br />
''Initial degenerations of Grassmannians''<br />
<br />
Let Gr_0(d,n) denote the open subvariety of the Grassmannian Gr(d,n) consisting of d-1 dimensional subspaces of P^{n-1} meeting the toric boundary transversely. We prove that Gr_0(3,7) is schoen in the sense that all of its initial degenerations are smooth. The main technique we will use is to express the initial degenerations of Gr_0(3,7) as a inverse limit of thin Schubert cells. We use this to show that the Chow quotient of Gr(3,7) by the maximal torus H in GL(7) is the log canonical compactification of the moduli space of 7 lines in P^2 in linear general position.<br />
<br />
===Alena Pirutka===<br />
<br />
"Irrationality problems"<br />
<br />
Let X be a projective algebraic variety, the set of solutions of a system of homogeneous polynomial equations. Several classical notions describe how ``unconstrained'' the solutions are, i.e., how close X is to projective space: there are notions of rational, unirational and stably rational varieties. Over the field of complex numbers, these notions coincide in dimensions one and two, but diverge in higher<br />
dimensions. In the last years, many new classes of non stably rational varieties were found, using a specialization technique, introduced by C. Voisin. This method also allowed to prove that the rationality is not a deformation invariant in smooth and projective families of complex varieties: this is a joint work with B. Hassett and Y. Tschinkel. In my talk I will describe classical examples, as well as the recent progress around these rationality questions.<br />
<br />
===Nero Budur===<br />
<br />
"Homotopy of singular algebraic varieties"<br />
By work of Simpson, Kollár, Kapovich, every finitely generated group can be the fundamental group of an irreducible complex algebraic variety with only normal crossings and Whitney umbrellas as singularities. In contrast, we show that if a complex algebraic variety has no weight zero 1-cohomology classes, then the fundamental group is strongly restricted: the irreducible components of the cohomology jump loci of rank one local systems containing the constant sheaf are complex affine tori. Same for links and Milnor fibers. This is joint work with Marcel Rubió.<br />
<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2018&diff=15442Algebra and Algebraic Geometry Seminar Spring 20182018-04-20T14:34:25Z<p>Wang: /* Spring 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B113.<br />
<br />
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]].<br />
<!--, [[Algebraic Geometry Seminar Spring 2018 | the next semester]], and for [[Algebraic Geometry Seminar | this semester]]. --><br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Spring 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|January 26<br />
|[http://homepages.math.uic.edu/~tmoulinos/ Tasos Moulinos (UIC)] <br />
|[[#Tasos Moulinos|Derived Azumaya Algebras and Twisted K-theory]]<br />
|Michael<br />
|-<br />
|February 2<br />
|Daniel Erman (Wisconsin) <br />
|[[#Daniel Erman|TBA]]<br />
|Local<br />
|-<br />
|'''February 8''' 2:30-3:30 in VV B113<br />
|[http://www.mathematics.pitt.edu/person/roman-fedorov/ Roman Fedorov (University of Pittsburgh)]<br />
|[[#Roman Fedorov|A conjecture of Grothendieck and Serre on principal bundles in mixed characteristic]]<br />
|Dima<br />
|-<br />
|February 9<br />
|Juliette Bruce (Wisconsin) <br />
|[[#Juliette Bruce|Asymptotic Syzygies in the Semi-Ample Setting ]]<br />
|Local<br />
|-<br />
|February 16<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Caldararu (Wisconsin)]<br />
|[[#Andrei Caldararu|Computing a categorical Gromov-Witten invariant]]<br />
|Local<br />
|-<br />
|February 23<br />
|Aron Heleodoro (Northwestern) <br />
|[[#Aron Heleodoro|Normally ordered tensor product of Tate objects and decomposition of higher adeles]]<br />
|Dima<br />
|-<br />
|March 2<br />
|Moisés Herradón Cueto (Wisconsin)<br />
|[[#Moisés Herradón Cueto|Local type of difference equations]]<br />
|Local<br />
|-<br />
|March 9<br />
|Eva Elduque (Wisconsin)<br />
|[[#Eva Elduque|On the signed Euler characteristic property for subvarieties of Abelian varieties]]<br />
|Local<br />
|-<br />
|March 16<br />
|[https://math.berkeley.edu/~chenhi/ Harrison Chen (Berkeley)]<br />
|[[#Harrison Chen|Equivariant localization for periodic cyclic homology and derived loop spaces]]<br />
|Andrei<br />
|-<br />
|March 23<br />
|[http://www-personal.umich.edu/~ptoste/ Phil Tosteson (Michigan)]<br />
|[[#Phil Tosteson|Stability in the homology of Deligne-Mumford compactifications]]<br />
|Steven<br />
|-<br />
|-<br />
|April 6<br />
|[http://www-personal.umich.edu/~weiho/ Wei Ho (Michigan)]<br />
|Noncommutative Galois closures and moduli problems<br />
|Daniel/Wanlin<br />
|-<br />
|-<br />
|April 13<br />
|[https://sites.google.com/site/dcorey2814/ Daniel Corey (Yale)]<br />
|[#Corey|Initial degenerations of Grassmannians]<br />
|Daniel<br />
|-<br />
|April 20<br />
|Alena Pirutka (NYU)<br />
|[[#Alena Pirutka|Irrationality problems]]<br />
|Jordan<br />
|-<br />
|'''April 23''' 2:30-3:30 at 225 Ingraham<br />
|Nero Budur (Leuven)<br />
|[[#Nero Budur|Homotopy of singular algebraic varieties]]<br />
|Botong<br />
|-<br />
|April 27<br />
|Alexander Yom Din (Caltech) <br />
|[[#Alexander Yom Din|Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules]]<br />
|Dima<br />
|-<br />
|May 4<br />
|John Lesieutre (UIC) <br />
|[[#John Lesieutre|TBA]]<br />
|Daniel<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Tasos Moulinos===<br />
<br />
'''Derived Azumaya Algebras and Twisted K-theory'''<br />
<br />
Topological K-theory of dg-categories is a localizing invariant of dg-categories over <math> \mathbb{C} </math><br />
taking values in the <math> \infty </math>-category of <math> KU </math>-modules. In this talk I describe a relative version<br />
of this construction; namely for <math>X</math> a quasi-compact, quasi-separated <math> \mathbb{C} </math>-scheme I construct a<br />
functor valued in the <math> \infty </math>-category of sheaves of spectra on <math> X(\mathbb{C}) </math>, the complex points of <math>X</math>. For inputs<br />
of the form <math>\operatorname{Perf}(X, A)</math> where <math>A</math> is an Azumaya algebra over <math>X</math>, I characterize the values<br />
of this functor in terms of the twisted topological K-theory of <math> X(\mathbb{C}) </math>. From this I deduce<br />
a certain decomposition, for <math> X </math> a finite CW-complex equipped with a bundle <math> P </math> of projective<br />
spaces over <math> X </math>, of <math> KU(P) </math> in terms of the twisted topological K-theory of <math> X </math> ; this is<br />
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer<br />
schemes.<br />
<br />
===Roman Fedorov===<br />
<br />
'''A conjecture of Grothendieck and Serre on principal bundles in mixed<br />
characteristic'''<br />
<br />
Let G be a reductive group scheme over a regular local ring R. An old<br />
conjecture of Grothendieck and Serre predicts that such a principal<br />
bundle is trivial, if it is trivial over the fraction field of R. The<br />
conjecture has recently been proved in the "geometric" case, that is,<br />
when R contains a field. In the remaining case, the difficulty comes<br />
from the fact, that the situation is more rigid, so that a certain<br />
general position argument does not go through. I will discuss this<br />
difficulty and a way to circumvent it to obtain some partial results.<br />
<br />
===Juliette Bruce===<br />
<br />
'''Asymptotic Syzygies in the Semi-Ample Setting'''<br />
<br />
In recent years numerous conjectures have been made describing the asymptotic Betti numbers of a projective variety as the embedding line bundle becomes more ample. I will discuss recent work attempting to generalize these conjectures to the case when the embedding line bundle becomes more semi-ample. (Recall a line bundle is semi-ample if a sufficiently large multiple is base point free.) In particular, I will discuss how the monomial methods of Ein, Erman, and Lazarsfeld used to prove non-vanishing results on projective space can be extended to prove non-vanishing results for products of projective space.<br />
<br />
===Andrei Caldararu===<br />
<br />
'''Computing a categorical Gromov-Witten invariant'''<br />
<br />
In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction to the derived category of sheaves of a complex projective variety provides a definition of higher genus B-model Gromov-Witten invariants, independent of the BCOV formalism. This has several advantages. Due to the categorical invariance of these invariants, categorical mirror symmetry automatically implies classical mirror symmetry to all genera. Also, the construction can be applied to other categories like categories of matrix factorization, giving a direct definition of FJRW invariants, for example.<br />
<br />
In my talk I shall describe the details of the computation (joint with Junwu Tu) of the invariant, at g=1, n=1, for elliptic curves. The result agrees with the predictions of mirror symmetry, matching classical calculations of Dijkgraaf. It is the first non-trivial computation of a categorical Gromov-Witten invariant.<br />
<br />
===Aron Heleodoro===<br />
<br />
'''Normally ordered tensor product of Tate objects and decomposition of higher adeles'''<br />
<br />
In this talk I will introduce the different tensor products that exist on Tate objects over vector spaces (or more generally coherent sheaves on a given scheme). As an application, I will explain how these can be used to describe higher adeles on an n-dimensional smooth scheme. Both Tate objects and higher adeles would be introduced in the talk. (This is based on joint work with Braunling, Groechenig and Wolfson.)<br />
<br />
===Moisés Herradón Cueto===<br />
<br />
'''Local type of difference equations'''<br />
<br />
The theory of algebraic differential equations on the affine line is very well-understood. In particular, there is a well-defined notion of restricting a D-module to a formal neighborhood of a point, and these restrictions are completely described by two vector spaces, called vanishing cycles and nearby cycles, and some maps between them. We give an analogous notion of "restriction to a formal disk" for difference equations that satisfies several desirable properties: first of all, a difference module can be recovered uniquely from its restriction to the complement of a point and its restriction to a formal disk around this point. Secondly, it gives rise to a local Mellin transform, which relates vanishing cycles of a difference module to nearby cycles of its Mellin transform. Since the Mellin transform of a difference module is a D-module, the Mellin transform brings us back to the familiar world of D-modules.<br />
<br />
===Eva Elduque===<br />
<br />
'''On the signed Euler characteristic property for subvarieties of Abelian varieties'''<br />
<br />
Franecki and Kapranov proved that the Euler characteristic of a perverse sheaf on a semi-abelian variety is non-negative. This result has several purely topological consequences regarding the sign of the (topological and intersection homology) Euler characteristic of a subvariety of an abelian variety, and it is natural to attempt to justify them by more elementary methods. In this talk, we'll explore the geometric tools used recently in the proof of the signed Euler<br />
characteristic property. Joint work with Christian Geske and Laurentiu Maxim.<br />
<br />
===Harrison Chen===<br />
<br />
'''Equivariant localization for periodic cyclic homology and derived loop spaces'''<br />
<br />
There is a close relationship between derived loop spaces, a geometric object, and (periodic) cyclic homology, a categorical invariant. In this talk we will discuss this relationship and how it leads to an equivariant localization result, which has an intuitive interpretation using the language of derived loop spaces. We discuss ongoing generalizations and potential applications in computing the periodic cyclic homology of categories of equivariant (coherent) sheaves on algebraic varieties.<br />
<br />
===Phil Tosteson===<br />
<br />
'''Stability in the homology of Deligne-Mumford compactifications'''<br />
<br />
The space <math>\bar M_{g,n}</math> is a compactification of the moduli space algebraic curves with marked points, obtained by allowing smooth curves to degenerate to nodal ones. We will talk about how the asymptotic behavior of its homology, <math>H_i(\bar M_{g,n})</math>, for <math>n \gg 0</math> can be studied using the representation theory of the category of finite sets and surjections.<br />
<br />
===Wei Ho===<br />
<br />
'''Noncommutative Galois closures and moduli problems'''<br />
<br />
In this talk, we will discuss the notion of a Galois closure for a possibly noncommutative algebra. We will explain how this problem is related to certain moduli problems involving genus one curves and torsors for Jacobians of higher genus curves. This is joint work with Matt Satriano.<br />
<br />
===Daniel Corey===<br />
<br />
''Initial degenerations of Grassmannians''<br />
<br />
Let Gr_0(d,n) denote the open subvariety of the Grassmannian Gr(d,n) consisting of d-1 dimensional subspaces of P^{n-1} meeting the toric boundary transversely. We prove that Gr_0(3,7) is schoen in the sense that all of its initial degenerations are smooth. The main technique we will use is to express the initial degenerations of Gr_0(3,7) as a inverse limit of thin Schubert cells. We use this to show that the Chow quotient of Gr(3,7) by the maximal torus H in GL(7) is the log canonical compactification of the moduli space of 7 lines in P^2 in linear general position.<br />
<br />
===Alena Pirutka===<br />
<br />
"Irrationality problems"<br />
<br />
Let X be a projective algebraic variety, the set of solutions of a system of homogeneous polynomial equations. Several classical notions describe how ``unconstrained'' the solutions are, i.e., how close X is to projective space: there are notions of rational, unirational and stably rational varieties. Over the field of complex numbers, these notions coincide in dimensions one and two, but diverge in higher<br />
dimensions. In the last years, many new classes of non stably rational varieties were found, using a specialization technique, introduced by C. Voisin. This method also allowed to prove that the rationality is not a deformation invariant in smooth and projective families of complex varieties: this is a joint work with B. Hassett and Y. Tschinkel. In my talk I will describe classical examples, as well as the recent progress around these rationality questions.<br />
<br />
===Alexander Yom Din===<br />
<br />
'''Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules'''<br />
<br />
Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.<br />
<br />
In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14823Colloquia/Fall182018-01-23T22:07:07Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Monday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14822Colloquia/Fall182018-01-23T21:51:54Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29 (Thursday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14821Colloquia/Fall182018-01-23T21:51:44Z<p>Wang: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 29(Thursday)<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
|February 9<br />
| [http://www.math.cmu.edu/~wes/ Wes Pegden] (CMU)<br />
|[[# TBA| TBA ]]<br />
| Roch<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|date<br />
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|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|[[# TBA| TBA ]]<br />
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|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
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|}<br />
<br />
<br />
== Spring Abstracts ==<br />
<br />
<DATE>: <PERSON> (INSTITUTION)<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14726Colloquia/Fall182018-01-06T00:06:45Z<p>Wang: /* Spring 2018 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Tonghai Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Paul Rabinowitz & Chanwoo Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Nigel Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Laurentiu Maxim<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Betsy Stovall, Andreas Seeger<br />
|<br />
|-<br />
|November 1 (Wednesday)<br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Andreas Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| Adhesion dynamics and the sticky particle system]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Projections in Banach Spaces and Harmonic Analysis ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday) '''9th floor'''<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday) '''B115'''<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday) '''9th floor'''<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Title: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: Adhesion dynamics and the sticky particle system.<br />
<br />
Abstract: The sticky particle system expresses the conservation of mass and<br />
momentum for a collection of particles that only interact via perfectly inelastic collisions. <br />
The equations were first considered in astronomy in a model for the expansion of <br />
matter without pressure. These equations also play a central role in the theory of optimal <br />
transport. Namely, the geodesics in an appropriately metrized space of probability <br />
measures correspond to solutions of the sticky particle system. We will survey what is <br />
known about solutions and discuss connections with Hamilton-Jacobi equations. <br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 13: Bobby Wilson (MIT)===<br />
Title: Projections in Banach Spaces and Harmonic Analysis<br />
<br />
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|January 30<br />
| [http://www.math.columbia.edu/~chaoli/ Li Chao] (Columbia)<br />
|[[# TBA| TBA ]]<br />
| Jordan Ellenberg<br />
|<br />
|-<br />
|February 2<br />
| [https://scholar.harvard.edu/tfai/home Thomas Fai] (Harvard)<br />
|[[# TBA| TBA ]]<br />
| Spagnolie, Smith<br />
|<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14661Colloquia/Fall182017-12-07T19:56:01Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Tonghai Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Paul Rabinowitz & Chanwoo Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Nigel Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Laurentiu Maxim<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Betsy Stovall, Andreas Seeger<br />
|<br />
|-<br />
|November 1 (Wednesday)<br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Andreas Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| Adhesion dynamics and the sticky particle system]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Projections in Banach Spaces and Harmonic Analysis ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday) '''9th floor'''<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday) '''B115'''<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday) '''9th floor'''<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Title: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: Adhesion dynamics and the sticky particle system.<br />
<br />
Abstract: The sticky particle system expresses the conservation of mass and<br />
momentum for a collection of particles that only interact via perfectly inelastic collisions. <br />
The equations were first considered in astronomy in a model for the expansion of <br />
matter without pressure. These equations also play a central role in the theory of optimal <br />
transport. Namely, the geodesics in an appropriately metrized space of probability <br />
measures correspond to solutions of the sticky particle system. We will survey what is <br />
known about solutions and discuss connections with Hamilton-Jacobi equations. <br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 13: Bobby Wilson (MIT)===<br />
Title: Projections in Banach Spaces and Harmonic Analysis<br />
<br />
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14609Colloquia/Fall182017-11-29T04:04:52Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | TBA ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14608Colloquia/Fall182017-11-29T04:03:13Z<p>Wang: Undo revision 14607 by Wang (talk)</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Stability in the homology of configuration spaces ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14607Colloquia/Fall182017-11-29T04:01:43Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Stability in the homology of configuration spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14606Colloquia/Fall182017-11-29T04:00:39Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Leslie Smith<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Stability in the homology of configuration spaces ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14605Colloquia/Fall182017-11-29T03:59:26Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8 (Friday)<br />
| [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)<br />
|[[#December 8: Nan Chen (Courant, NYU)| A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]<br />
|Sigurd Angenent<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | Stability in the homology of configuration spaces ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 8: Nan Chen (Courant, NYU)===<br />
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems<br />
<br />
Abstract:<br />
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. <br />
<br />
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14604Colloquia/Fall182017-11-29T03:52:20Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | TBA ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
===December 15: Roy Lederman (Princeton)===<br />
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)<br />
<br />
Abstract:<br />
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". <br />
<br />
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. <br />
<br />
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. <br />
<br />
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14603Colloquia/Fall182017-11-29T03:50:46Z<p>Wang: /* Mathematics Colloquium */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Regularity vs. Singularity for Elliptic and Parabolic Systems]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 13 (Wednesday)<br />
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)<br />
|[[#December 13: Bobby Wilson (MIT) | TBA ]]<br />
|Andreas Seeger<br />
|<br />
|-<br />
|December 15 (Friday)<br />
| [http://roy.lederman.name/ Roy Lederman] (Princeton)<br />
|[[#December 15: Roy Lederman | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]<br />
|Leslie Smith<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14593Colloquia/Fall182017-11-26T17:45:05Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins (Harvard)| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14592Colloquia/Fall182017-11-26T17:44:21Z<p>Wang: /* November 27:Tristan Collins */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins (Harvard)] (Harvard)<br />
|[[#November 27:Tristan Collins| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins (Harvard)===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14591Colloquia/Fall182017-11-26T17:44:01Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins (Harvard)] (Harvard)<br />
|[[#November 27:Tristan Collins| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation. <br />
<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wanghttp://www.math.wisc.edu/wiki/index.php?title=Colloquia/Fall18&diff=14590Colloquia/Fall182017-11-26T17:43:25Z<p>Wang: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1, <br />
|[http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)<br />
|[[#November 1: Shaoming Guo (Indiana)| Parsell-Vinogradov systems in higher dimensions ]]<br />
|Seeger<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 17<br />
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)<br />
|[[#November 17:Yevgeny Liokumovich (MIT)| Recent progress in Min-Max Theory ]]<br />
|Sean Paul<br />
|-<br />
|November 21, '''9th floor'''<br />
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)<br />
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces ]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|<br />
|<br />
|-<br />
|November 27, <br />
| [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)<br />
|[[#November 27:Tristan Collins| The J-equation and stability ]]<br />
|Sean Paul<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|-<br />
|December 5 (Tuesday)<br />
| [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)<br />
|[[#December 5: Ryan Hynd (U Penn)| TBA ]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 11 (Monday)<br />
| [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)<br />
|[[#December 11: Connor Mooney (ETH Zurich)| Finite time blowup for parabolic systems in the plane]]<br />
|Sigurd Angenent<br />
|<br />
|-<br />
|December 18 (Monday)<br />
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)<br />
|[[#December 18: Jenny Wilson (Stanford)| Stability in the homology of configuration spaces]]<br />
|Jordan Ellenberg<br />
|<br />
|-<br />
|December 19 (Tuesday)<br />
| [https://web.stanford.edu/~amwright/ Alex Wright] (Stanford)<br />
|[[#December 19: Alex Wright (Stanford)| Dynamics, geometry, and the moduli space of Riemann surfaces]]<br />
|Jordan Ellenberg<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
<br />
<br />
===October 20: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
===October 27: Stefanie Petermichl (Toulouse)===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===November 1: Shaoming Guo (Indiana) ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===November 17:Yevgeny Liokumovich (MIT)===<br />
Title: Recent progress in Min-Max Theory<br />
<br />
Abstract:<br />
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?<br />
<br />
===November 21:Michael Kemeny (Stanford)===<br />
Title: The equations defining curves and moduli spaces<br />
<br />
Abstract:<br />
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with<br />
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures<br />
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,<br />
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.<br />
<br />
<br />
===November 27:Tristan Collins===<br />
Titile: The J-equation and stability<br />
<br />
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation. <br />
<br />
<br />
===December 5: Ryan Hynd (U Penn)===<br />
Title: TBA.<br />
<br />
===December 11: Connor Mooney (ETH Zurich)===<br />
Title: Finite time blowup for parabolic systems in the plane<br />
<br />
Abstract:<br />
Hilbert's 19th problem asks about the smoothness of solutions to nonlinear elliptic PDE that arise in the calculus of variations. This problem leads naturally to the question of continuity for solutions to linear elliptic and parabolic systems with measurable coefficients. We will first discuss some classical results on this topic, including Morrey's result that solutions to linear elliptic systems in two dimensions are continuous. We will then discuss surprising recent examples of finite time blowup from smooth data for linear parabolic systems in two dimensions, and important open problems.<br />
<br />
<br />
===December 18: Jenny Wilson (Stanford)===<br />
Title: Stability in the homology of configuration spaces<br />
<br />
Abstract: <br />
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.<br />
<br />
===December 19: Alex Wright (Stanford)===<br />
Title: Dynamics, geometry, and the moduli space of Riemann surfaces<br />
<br />
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel. <br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|April 4 (Wednesday)<br />
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
| April 13<br />
| [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 25 (Wednesday)<br />
| Hitoshi Ishii (Waseda University) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Tran<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Wang