http://www.math.wisc.edu/wiki/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=UW-Math Wiki - New pages [en]2019-08-24T15:24:00ZFrom UW-Math WikiMediaWiki 1.30.1http://www.math.wisc.edu/wiki/index.php/Geometry_and_Topology_Seminar_2018-2019Geometry and Topology Seminar 2018-20192019-08-22T14:17:57Z<p>Dymarz: Created page with "The Geometry and Topology seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''. <br> For more information, contact Shaosai Huang...."</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2019 ==<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|April 5<br />
|Mark Pengitore (Ohio)<br />
|Translation-like actions on nilpotent groups<br />
<br />
|(Dymarz)<br />
|-<br />
|April 18<br />
|José Ignacio Cogolludo Agustín (Universidad de Zaragoza)<br />
|Even Artin Groups, cohomological computations and other geometrical properties.<br />
<br />
|(Maxim)<br />
|'''Unusual date and time: B309 Van Vleck, 2:15-3:15'''<br />
|-<br />
<br />
|April 19<br />
|Yan Xu (University of Missouri - St. Louis)<br />
|Structure of minimal two-spheres of constant curvature in hyperquadrics<br />
|(Huang)<br />
<br />
|}<br />
<br />
== Fall 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept. 14<br />
|Teddy Einstein (UIC)<br />
|Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes<br />
|(Dymarz)<br />
|-<br />
|Oct. 12<br />
|Marissa Loving <br />
|Least dilatation of pure surface braids<br />
|(Kent)<br />
|-<br />
|Oct. 19<br />
|Sara Maloni <br />
|On type-preserving representations of thrice punctured projective plane group<br />
|(Kent)<br />
|-<br />
|Oct. 26<br />
|Dingxin Zhang (Harvard-CMSA)<br />
|Relative cohomology and A-hypergeometric equations<br />
|(Huang)<br />
|-<br />
|Nov. 9<br />
|Zhongshan An (Stony Brook)<br />
|Ellipticity of the Bartnik Boundary Conditions<br />
|(Huang)<br />
|-<br />
|Nov. 16<br />
|Xiangdong Xie<br />
|Quasi-isometric rigidity of a class of right angled Coxeter groups<br />
|(Dymarz)<br />
|-<br />
|<br />
|}<br />
<br />
<br />
==Spring Abstracts==<br />
<br />
===Mark Pengitore===<br />
<br />
"Translation-like actions on nilpotent groups"<br />
<br />
Translation-like actions were introduced Whyte to generalize subgroup containment. Using this notion, he proved that a group is non-amenable if and only if it admits a translation-like action by a non-abelian free group. This result motivates us to ask what groups admit translation-like actions on various interesting classes of groups. As a consequence of Gromov's polynomial growth theorem, we have that only nilpotent groups may act translation-like on a nilpotent group which is the main focus of this talk. Thus, one may ask to characterize what nilpotent groups act translation-like on a fixed nilpotent group. We offer partial answer to this question by demonstrating that if two nilpotent groups have the same growth but distinct asymptotic cones, then there exist no translation-like action of these two groups on each other.<br />
<br />
===José Ignacio Cogolludo Agustín===<br />
<br />
"Even Artin Groups, cohomological computations and other geometrical <br />
properties."<br />
<br />
The purpose of this talk is to introduce even Artin groups and consider<br />
their quasi-projectivity properties, as well as study the cohomological <br />
properties of their kernels, that is, the kernels of their characters.<br />
<br />
===Yan Xu===<br />
"Structure of minimal two-spheres of constant curvature in hyperquadrics"<br />
<br />
Veronese two-sphere (also called rational normal curve) is an interesting projective variety in geometry. It is of constant curvature and unique up to action of unitary group. Based on this rigidity result and SVD (singular value decomposition) in linear algebra, we give a classification of a special class minimal, especially holomorphic, two-spheres of constant curvature in hyperquadric, up to action of real orthogonal group and reparameterization of the two-sphere. For degree less than or equal to three, we give an algorithm and explicit examples. As an application of this results, by computing the norm squared of second fundamental form, we show the generic two-spheres constructed here are not homogeneous. This is a joint work with Professor Quo-Shin Chi and Zhenxiao Xie.<br />
<br />
== Fall Abstracts ==<br />
<br />
===Teddy Einstein===<br />
<br />
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"<br />
<br />
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.<br />
<br />
===Marissa Loving===<br />
<br />
"Least dilatation of pure surface braids"<br />
<br />
The n-stranded pure surface braid group of a genus g surface can be described as the subgroup of the pure mapping class group of a surface of genus g with n-punctures which becomes trivial on the closed surface. I am interested in the least dilatation of pseudo-Anosov pure surface braids. For the n=1 case, upper and lower bounds on the least dilatation were proved by Dowdall and Aougab—Taylor, respectively. In this talk, I will describe the upper and lower bounds I have proved as a function of g and n.<br />
<br />
===Sara Maloni===<br />
<br />
"On type-preserving representations of thrice punctured projective plane group"<br />
<br />
In this talk, after a brief overview on famous topological and dynamical open questions on character varieties, we will consider type-preserving representations of the fundamental group of the three-holed projective plane N into PGL(2, R). First, we prove Kashaev’s conjecture on the number of connected components with non-maximal euler class. Second, we show that for all representations with euler class 0 there is a one simple closed curve which is sent to a non-hyperbolic element, while in euler class 1 or -1 we show that there are six components where all the simple closed curves are sent to hyperbolic elements and 2 components where there are some simple closed curves sent to non-hyperbolic elements. This answers a generalisation of a question asked by Bowditch for orientable surfaces. In addition, we show, in most cases, that the action of the pure mapping class group Mod(N) on these non-maximal components is ergodic, proving Goldman conjecture in those cases. Time permitting we will discuss a work in progress with Palesi where we expend these results to all five surfaces (orientable and non-orientable) of characteristic -2. (This is joint work with F. Palesi and T. Yang.)<br />
<br />
===Dingxin Zhang===<br />
"Relative cohomology and A-hypergeometric equations"<br />
<br />
The GKZ hypergeometric equations are closely related to the period integrals of algebraic varieties. Based on the theorems of Walther--Schulze, we identify the set of solutions of a certain GKZ system with some relative homology groups. Our result generalizes the theorem of Huang--Lian--Yau--Zhu. This is a joint work with Tsung-Ju Lee.<br />
<br />
<br />
===Zhongshan An===<br />
"Ellipticity of the Bartnik Boundary Conditions"<br />
<br />
The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data — the so-called Bartnik boundary data— plays a key role. Bartnik proposed the open problem whether, on a given manifold with boundary, there exists a stationary vacuum metric so that the Bartnik boundary conditions are realized. In the effort to answer this question, it is important to prove the ellipticity of Bartnik boundary conditions for stationary vacuum metrics. In this talk, I will start with an introduction to the Bartnik quasi-local mass and the moduli space of stationary vacuum metrics. Then I will explain the ellipticity result for the Bartnik boundary conditions and, as an application, give a partial answer to the existence question.<br />
<br />
===Xiangdong Xie===<br />
"Quasi-isometric rigidity of a class of right angled Coxeter groups"<br />
<br />
Given any finite simplicial graph G with vertex set V and edge set E, the associated right angled Coxeter group (RACG) W(G) is defined <br />
as the group with generating set V whose generators all have order 2 and where uv=vu for each edge (u,v).<br />
The classical examples are the reflection groups generated by the reflections about edges of right angled polygons (in the Euclidean plane or the hyperbolic plane). We classify a class of RACGs up to quasi-isometry. This is joint work with Jordan Bounds.<br />
<br />
== Spring Abstracts ==<br />
<br />
== Archive of past Geometry seminars ==<br />
<br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
2010: [[Fall-2010-Geometry-Topology]]</div>Dymarzhttp://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2019NTSGrad Fall 20192019-08-12T23:12:20Z<p>Soumyasankar: /* Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting some mini SAGE workshops. If you would like to participate in these, please email the organizers.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|TBA<br />
| bgcolor="#BCD2EE" width="300" align="center"|TBA<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| TBA<br />
| bgcolor="#BCD2EE" width="300" align="center"| TBA<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttp://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Spring_2020Algebra and Algebraic Geometry Seminar Spring 20202019-08-02T11:57:59Z<p>Derman: /* Spring 2020 Schedule */</p>
<hr />
<div>== Spring 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|February 7<br />
|Jonathan Monta&#241;o<br />
|<br />
|<br />
|-<br />
|February 14<br />
|<br />
|<br />
| <br />
|-<br />
|February 21<br />
|<br />
|<br />
|<br />
|-<br />
|February 28<br />
|<br />
|<br />
|<br />
|-<br />
|March 6<br />
|<br />
|<br />
|<br />
|-<br />
|March 13<br />
|<br />
|<br />
|<br />
|-<br />
|March 20<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|<br />
|<br />
|<br />
|-<br />
|April 3<br />
|<br />
|<br />
|<br />
|-<br />
|April 10<br />
|<br />
|<br />
|<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|<br />
|<br />
|<br />
|-<br />
|May 1<br />
|Lazarsfeld Distinguished Lectures<br />
|<br />
|<br />
|-<br />
|May 8<br />
|<br />
|<br />
| <br />
|-<br />
|}</div>Dermanhttp://www.math.wisc.edu/wiki/index.php/Applied/ACMS/Spring2020Applied/ACMS/Spring20202019-07-25T14:13:13Z<p>Spagnolie: /* Spring 2020 */</p>
<hr />
<div>== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Jan 31<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Feb 7<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Feb 14<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Feb 21<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Feb 28<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Mar 6<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Mar 13<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Mar 20<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Mar 27<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Apr 3<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Apr 10<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Apr 17<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host<br />
|-<br />
| Apr 24<br />
|[website] (institution)<br />
|''[[Applied/ACMS/absS20#Speaker (institution)|title]]''<br />
| host</div>Spagnoliehttp://www.math.wisc.edu/wiki/index.php/CCA_Reading_GroupCCA Reading Group2019-07-16T17:38:21Z<p>Cbooms: </p>
<hr />
<div>This is the page for the Fall 2019 Computational Commutative Algebra Reading Group, which is open to all UW Math grad students, but will require a certain amount of participation and work to receive credit.<br />
<br />
== Resources ==<br />
<br />
We plan to read Cox, Little, and O'Shea's ''Ideals, Varieties, and Algorithms'', which can be found here: [https://doc.lagout.org/science/0_Computer%20Science/2_Algorithms/Ideals%2C%20Varieties%2C%20and%20Algorithms%20%284th%20ed.%29%20%5BCox%2C%20Little%20%26%20O%27Shea%202015-06-14%5D.pdf].<br />
<br />
== Meeting Schedule ==<br />
<br />
10 weeks total, starting the week of Sept. 9, adjusting throughout the semester.<br />
<br />
Meetings twice per week for an hour, days and times TBD depending on participants' schedules.<br />
<br />
Exact schedule may vary slightly from week to week as needed.<br />
<br />
<br />
'''Approximate Reading Schedule:'''<br />
<br />
1. Ch. 2: Grobner Bases, Sections 1-3<br />
<br />
2. Ch. 2: Grobner Bases, Sections 4-6<br />
<br />
3. Ch. 2: Grobner Bases, Sections 7-8<br />
<br />
4. Exercises<br />
<br />
5. Ch. 3: Elimination Theory, Sections 1-3<br />
<br />
6. Ch. 3: Elimination Theory, Sections 4-6<br />
<br />
7. Ch. 4: The Algebra-Geometry Dictionary, Sections 1-3<br />
<br />
8. Ch. 4: The Algebra-Geometry Dictionary, Sections 4-6<br />
<br />
8. Ch. 4: The Algebra-Geometry Dictionary, Sections 7-9<br />
<br />
9. Catch up/guest lecture<br />
<br />
10. Catch up/guest lecture<br />
<br />
11. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 1-3<br />
<br />
12. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 4-6<br />
<br />
13. Ch. 8: Projective Algebraic Geometry, Sections 1-4<br />
<br />
14. Ch. 8: Projective Algebraic Geometry, Sections 5-7<br />
<br />
15. Exercises<br />
<br />
16. Ch. 9: The Dimension of a Variety, Sections 1-3<br />
<br />
17. Ch. 9: The Dimension of a Variety, Sections 4-6<br />
<br />
18. Exercises<br />
<br />
19. Catch up/guest lecture<br />
<br />
20. Catch up/guest lecture<br />
<br />
== General Meeting Structure ==<br />
<br />
This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be an older grad student or professor. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be pretty flexible and will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We will also use Macaulay2 during the exercise sessions to get comfortable both computing examples by hand and by using a computer.<br />
<br />
'''If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu by Sept. 4, 2019.'''</div>Cboomshttp://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2019NTS ABSTRACTFall20192019-07-16T16:07:10Z<p>Shusterman: /* Sep 5 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Sawin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The sup-norm problem for automorphic forms over function fields and geometry<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The sup-norm problem is a purely analytic question about <br />
automorphic forms, which asks for bounds on their largest value (when <br />
viewed as a function on a modular curve or similar space). We describe <br />
a new approach to this problem in the function field setting, which we <br />
carry through to provide new bounds for forms in GL_2 stronger than <br />
what can be proved for the analogous question about classical modular <br />
forms. This approach proceeds by viewing the automorphic form as a <br />
geometric object, following Drinfeld. It should be possible to prove <br />
bounds in greater generality by this approach in the future.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Shustermanhttp://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019NTS Spring Semester 20192019-07-16T15:34:02Z<p>Shusterman: Created page with "= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison = *'''When:''' Thursdays, 2:30 PM – 3:30 PM *'''Where:''' Van Vleck B113 *Please join th..."</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B113<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2019 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Fall 2018 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_2018_Semester Spring 2018].<br />
<br />
= Spring 2019 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 23<br />
'''Wed. Room VV B231'''<br />
| bgcolor="#F0B0B0" align="center" | [http://web.math.princeton.edu/~yunqingt/ Yunqing Tang (Princeton University)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Jan_23 Reductions of abelian surfaces over global function fields]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 24<br />
| bgcolor="#F0B0B0" align="center" | Hassan-Mao-Smith--Zhu<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Jan_24 The diophantine exponent of the $\mathbb{Z}/q\mathbb{Z}$ points of $S^{d-2}\subset S^d$]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 31<br />
| bgcolor="#F0B0B0" align="center" | [https://faculty.math.illinois.edu/~kpratt4/ Kyle Pratt (University of Illinois at Urbana-Champaign)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Jan_31 Breaking the $\frac{1}{2}$-barrier for the twisted second moment of Dirichlet $L$-functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 7 <br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~shamgar/ Shamgar Gurevich (UW-Madison)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Feb_7 Harmonic Analysis on $GL_n$ over finite fields] <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 14<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~thyang/ Tonghai Yang (UW-Madison)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Feb_14 The Lambda invariant and its CM values]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 21<br />
| bgcolor="#F0B0B0" align="center" | No Seminar<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 28<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.columbia.edu/~brianrl/ Brian Lawrence (the University of Chicago)] <br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#Feb_28 Diophantine problems and a p-adic period map.] <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 7<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/masoudzargar/ Masoud Zargar (Regensburg)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#March_7 Sections of quadrics over the affine line] <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 14<br />
| bgcolor="#F0B0B0" align="center" | [http://www.its.caltech.edu/~mantovan/ Elena Mantovan (Caltech)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#March_14 p-adic automorphic forms, differential operators and Galois representations]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 21<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 28<br />
| bgcolor="#F0B0B0" align="center" | [http://web.math.ucsb.edu/~agboola/ Adebisi Agboola (UCSB)] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#March_28 Relative K-groups and rings of integers]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 4<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.tamu.edu/~wltsai/ Wei-Lun Tsai (Texas A&M University)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_4 Hecke L-functions and $\ell$ torsion in class groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 11<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.ucsd.edu/~tmcadam/ Taylor McAdam (UCSD)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_11 Almost-prime times in horospherical flows]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 18 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.ucsd.edu/~ila/ Ila Varma (UCSD)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_18 Malle's Conjecture for octic $D_4$-fields.]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
'''10:00-11:00 Room VV 911'''<br />
| bgcolor="#F0B0B0" align="center" | [https://bushm.academic.wlu.edu Michael Bush (Washington & Lee)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_25 Interactions between group theory and number theory]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
'''11:15-12:15 Room VV 911'''<br />
| bgcolor="#F0B0B0" align="center" | [https://people.carleton.edu/~rfjones/ Rafe Jones (Carleton College)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_25_2 Eventually stable polynomials and arboreal Galois representations]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
| bgcolor="#F0B0B0" align="center" | [https://math.rice.edu/~jb93/ Jen Berg (Rice University)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_25_NTS Rational points on conic bundles over elliptic curves with positive rank] <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 25<br />
'''4:00-5:00 Room VV B239'''<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.unl.edu/~jwalker7/ Judy Walker (Nebraska)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#April_25_3 Derangements of Finite Groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 2<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~mmwood/ Melanie Wood (UW-Madison)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#May_2 Unramified extensions of random global fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 9 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.mathcs.emory.edu/~dzb/ David Zureick-Brown (Emory College of Arts and Sciences)]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2019#May_9 Arithmetic of stacks] <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~ntalebiz/ Naser Talebizadeh Sardari]<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<br />
<br />
[http://www.math.wisc.edu/~ruixiang/ Ruixiang Zhang]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shustermanhttp://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Fall_2019Algebra and Algebraic Geometry Seminar Fall 20192019-06-15T13:33:41Z<p>Arinkin: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room TBA.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | 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 />
== Fall 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 />
|September 6<br />
|<br />
|<br />
| Reserved (Dima)<br />
|-<br />
|September 13<br />
|<br />
|<br />
| Reserved (Juliette)<br />
|-<br />
|September 20<br />
|<br />
|<br />
|<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|<br />
|<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|<br />
|<br />
|<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|<br />
|<br />
|<br />
|-<br />
|November 29<br />
|<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker===<br />
'''Title: '''<br />
Abstract:</div>Juliettebrucehttp://www.math.wisc.edu/wiki/index.php/Fall_2018_and_Spring_2019_Analysis_SeminarsFall 2018 and Spring 2019 Analysis Seminars2019-06-03T20:42:04Z<p>Nagreen: Created page with "'''Analysis Seminar ''' The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated. If you wish to invite a speaker please contact Brian at street(a..."</p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|*[https://www.math.wisc.edu/seeger2019/?q=node/2 Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|-<br />
|Oct 15<br />
|Bassam Shayya<br />
|American University of Beirut<br />
|<br />
|Andreas, Betsy<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
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<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
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In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
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<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.</div>Nagreen