https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Derman&feedformat=atomUW-Math Wiki - User contributions [en]2019-12-08T23:03:55ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18512Colloquia2019-12-02T14:41:11Z<p>Derman: /* Mathematics Colloquium */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan<br />
|Flag varieties and representations of p-adic groups<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18511Colloquia2019-12-02T14:40:42Z<p>Derman: /* Charlotte Chain (MIT) */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18510Colloquia2019-12-02T14:40:37Z<p>Derman: /* Andrew Zimmer (LSU) */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chain (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18413Algebra and Algebraic Geometry Seminar Fall 20192019-11-15T02:05:56Z<p>Derman: /* Libby Taylor */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Libby Taylor<br />
|<math>\mathbb{A}^1</math>-local degree via stacks<br />
|Daniel/Soumya<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|Cynthia Vinzant<br />
|TBD<br />
| Matroids Day<br />
|-<br />
|December 13<br />
|Taylor Brysiewicz<br />
|The degrees of Stiefel manifolds<br />
| Jose<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
===Libby Taylor===<br />
'''<math>\mathbb{A}^1</math>-local degree via stacks'''<br />
<br />
We extend results of Kass-Wickelgren to define an Euler class for a non-orientable vector bundle on a smooth scheme, valued in the Grothendieck-Witt group of the ground field. We use a root stack construction to produce this Euler class and discuss its relation to <math>\mathbb{A}^1</math>-homotopy-theoretic definitions of an Euler class. This allows one to apply Kass-Wickelgren's technique for arithmetic enrichments of enumerative geometry to a larger class of problems; as an example, we use our construction to give an arithmetic count of the number of lines meeting $6$ planes in <math>\mathbb{P}^4</math>.<br />
<br />
===Taylor Brysiewicz===<br />
'''The degrees of Stiefel manifolds'''<br />
<br />
The Stiefel manifold of orthonormal bases for k-planes in an n-dimensional space goes by a different name in the world of frame theory: the space of Parseval n-frames for a k-dimensional space. The Stiefel manifold, and many other spaces of finite frames, can be viewed as an algebraic variety embedded in the space of k by n matrices. This viewpoint is known as algebraic frame theory and still many algebro-geometric properties of these varieties remain unknown, in particular, their degrees. As a first step in understanding these varieties, we compute a formula for the degrees of Stiefel manifolds using techniques from classical algebraic geometry, representation theory, and combinatorics. This is joint work with Fulvio Gesmundo.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=18403Algebra and Algebraic Geometry Seminar Spring 20202019-11-12T14:53:17Z<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 />
|January 24<br />
|Xi Chen (Alberta)<br />
|TBD<br />
|Michael K<br />
|-<br />
|January 31<br />
|Janina Letz (Utah)<br />
|TBD<br />
|Daniel and Michael B<br />
|-<br />
|February 7<br />
|Jonathan Monta&#241;o (New Mexico State)<br />
|TBD<br />
|Daniel<br />
|-<br />
|February 14<br />
|<br />
|<br />
| <br />
|-<br />
|February 21<br />
|Erika Ordog (Duke)<br />
|TBD<br />
|Daniel<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18376Colloquia2019-11-08T20:16:15Z<p>Derman: /* Fall 2019 */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18375Colloquia2019-11-08T19:20:52Z<p>Derman: /* Fall 2019 */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18374Colloquia2019-11-08T19:20:20Z<p>Derman: /* Jose Rodriguez (UW-Madison) */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18348Algebra and Algebraic Geometry Seminar Fall 20192019-11-07T16:12:31Z<p>Derman: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Libby Taylor<br />
|TBD<br />
|Daniel/Soumya<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|Cynthia Vinzant<br />
|TBD<br />
| Matroids Day<br />
|-<br />
|December 13<br />
|Taylor Brysiewicz<br />
|<br />
| Jose<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18300Colloquia2019-11-04T03:24:50Z<p>Derman: /* Shamgar Gurevich (Madison) */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18299Colloquia2019-11-04T03:23:02Z<p>Derman: /* Fall 2019 */</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 />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "TBA"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==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 />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite 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 character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: TBA<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18281Algebra and Algebraic Geometry Seminar Fall 20192019-10-31T11:30:20Z<p>Derman: /* Michael Brown */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Reserved<br />
|TBD<br />
|(Jose)<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|RESERVED<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18280Algebra and Algebraic Geometry Seminar Fall 20192019-10-31T11:29:45Z<p>Derman: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Reserved<br />
|TBD<br />
|(Jose)<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|RESERVED<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17831Madison Math Circle2019-09-12T13:48:53Z<p>Derman: /* Meetings for Fall 2019 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || Soumya Sankar || TBD<br />
|-<br />
| September 30, 2019 || TBD || TBD<br />
|-<br />
| October 7, 2019 || Uri Andrews || TBD<br />
|-<br />
| October 14, 2019 || TBD || TBD<br />
|-<br />
| October 21, 2019 || TBD || TBD<br />
|-<br />
| October 28, 2019 || TBD || TBD<br />
|-<br />
| November 4, 2019 || Omer Merlstein || TBD<br />
|-<br />
| November 11, 2019 || TBD || TBD<br />
|-<br />
| November 18, 2019 || Daniel Corey || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us! TBD.<br />
<br />
<br />
<center><br />
<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17830Madison Math Circle2019-09-12T13:47:53Z<p>Derman: /* Meetings for Fall 2019 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || Soumya Sankar || TBD<br />
|-<br />
| September 30, 2019 || TBD || TBD<br />
|-<br />
| October 7, 2019 || TBD || TBD<br />
|-<br />
| October 14, 2019 || TBD || TBD<br />
|-<br />
| October 21, 2019 || TBD || TBD<br />
|-<br />
| October 28, 2019 || TBD || TBD<br />
|-<br />
| November 4, 2019 || Omer Merlstein || TBD<br />
|-<br />
| November 11, 2019 || TBD || TBD<br />
|-<br />
| November 18, 2019 || Daniel Corey || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us! TBD.<br />
<br />
<br />
<center><br />
<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=17814Algebra and Algebraic Geometry Seminar Spring 20202019-09-11T19:23:54Z<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 />
|January 24<br />
|<br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|Jonathan Monta&#241;o<br />
|TBD<br />
|Daniel<br />
|-<br />
|February 14<br />
|<br />
|<br />
| <br />
|-<br />
|February 21<br />
|Erika Ordog (Duke)<br />
|TBD<br />
|Daniel<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17810Algebra and Algebraic Geometry Seminar Fall 20192019-09-11T11:21:06Z<p>Derman: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|TBD<br />
|Daniel<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|RESERVED<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=17809Algebra and Algebraic Geometry Seminar Spring 20202019-09-11T11:11:22Z<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 />
|January 24<br />
|<br />
|<br />
|<br />
|-<br />
|January 31<br />
|<br />
|<br />
|<br />
|-<br />
|February 7<br />
|Jonathan Monta&#241;o<br />
|TBD<br />
|Daniel<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17808Algebra and Algebraic Geometry Seminar Fall 20192019-09-11T11:09:26Z<p>Derman: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|TBD<br />
|Daniel<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|RESERVED<br />
|<br />
| Reserved (Matroids Day)<br />
|-<br />
|December 13<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17807Algebra and Algebraic Geometry Seminar Fall 20192019-09-11T11:08:06Z<p>Derman: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|<br />
|<br />
|<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|TBD<br />
|Daniel<br />
|-<br />
|November 15<br />
|Erika Ordog (Duke)<br />
|TBD<br />
|Daniel<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<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 />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17802Algebra and Algebraic Geometry Seminar Fall 20192019-09-10T01:55:16Z<p>Derman: /* Juliette Bruce */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<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 />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17801Algebra and Algebraic Geometry Seminar Fall 20192019-09-10T01:54:44Z<p>Derman: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<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 />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<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 />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|<br />
|<br />
|-<br />
|November 15<br />
|<br />
|<br />
|<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<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 />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17798Madison Math Circle2019-09-09T21:52:29Z<p>Derman: /* Off-Site Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2018<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || TBD || TBD<br />
|-<br />
| September 30, 2019 || TBD || TBD<br />
|-<br />
| October 7, 2019 || TBD || TBD<br />
|-<br />
| October 14, 2019 || TBD || TBD<br />
|-<br />
| October 21, 2019 || TBD || TBD<br />
|-<br />
| October 28, 2019 || TBD || TBD<br />
|-<br />
| November 4, 2019 || TBD || TBD<br />
|-<br />
| November 11, 2019 || TBD || TBD<br />
|-<br />
| November 18, 2019 || TBD || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us! TBD.<br />
<br />
<br />
<center><br />
<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17797Madison Math Circle2019-09-09T21:52:09Z<p>Derman: /* Meetings for Fall 2019 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2018<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || TBD || TBD<br />
|-<br />
| September 30, 2019 || TBD || TBD<br />
|-<br />
| October 7, 2019 || TBD || TBD<br />
|-<br />
| October 14, 2019 || TBD || TBD<br />
|-<br />
| October 21, 2019 || TBD || TBD<br />
|-<br />
| October 28, 2019 || TBD || TBD<br />
|-<br />
| November 4, 2019 || TBD || TBD<br />
|-<br />
| November 11, 2019 || TBD || TBD<br />
|-<br />
| November 18, 2019 || TBD || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2017<br />
|-<br />
|-<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
|-<br />
| October 29th || 2:45pm|| East High School - Madison, WI || TBD || TBD <br />
|-<br />
| December 3rd || 2:45pm|| East High School - Madison, WI || TBD || TBD<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17796Madison Math Circle2019-09-09T21:51:58Z<p>Derman: /* Meetings for Spring 2019 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2018<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || TBD || TBD<br />
|-<br />
| September 30, 2019 || TBD || TBD<br />
|-<br />
| October 7, 2019 || TBD || TBD<br />
|-<br />
| October 14, 2019 || TBD || TBD<br />
|-<br />
| October 21, 2019 || TBD || TBD<br />
|-<br />
| October 28, 2019 || TBD || TBD<br />
|<br />
| November 4, 2019 || TBD || TBD<br />
|-<br />
| November 11, 2019 || TBD || TBD<br />
|-<br />
| November 18, 2019 || TBD || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2017<br />
|-<br />
|-<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
|-<br />
| October 29th || 2:45pm|| East High School - Madison, WI || TBD || TBD <br />
|-<br />
| December 3rd || 2:45pm|| East High School - Madison, WI || TBD || TBD<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17795Madison Math Circle2019-09-09T21:50:02Z<p>Derman: /* Meetings for Fall 2018 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Spring 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2019<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| January 28, 2019 || CANCELLED || Madison's schools are closed<br />
|-<br />
| February 4, 2019 || Stephen Davis || Newton's law of gravity<br />
|-<br />
| February 11, 2019 || Yandi Wu || Surfaces and "Cut and Paste Topology"<br />
|-<br />
| February 18, 2019 || Michel Alexis || Kakeya Needle Sets<br />
|-<br />
| February 25, 2019 || Colin Crowley || Regular Languages<br />
|-<br />
| March 4, 2019 || Jenny Yeon || Where do numbers like "1/3" and "1/4" in volume formulas come from?<br />
|-<br />
| March 11, 2019 || Chaojie Yuan || A region of finite area with infinite perimeter<br />
|-<br />
| March 18, 2019 || No Meeting || Spring Break<br />
|-<br />
| March 25, 2019 || Eva Elduque || Will it fold flat?<br />
|-<br />
| April 1, 2019 || Alex Mine || Cellular Automata<br />
|-<br />
| April 8, 2019 || Caitlyn Booms || Pile Splitting<br />
|-<br />
| April 15, 2019 || Polly Yu || Chaos and unavoidable patterns<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2017<br />
|-<br />
|-<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
|-<br />
| October 29th || 2:45pm|| East High School - Madison, WI || TBD || TBD <br />
|-<br />
| December 3rd || 2:45pm|| East High School - Madison, WI || TBD || TBD<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17624Algebra and Algebraic Geometry Seminar Fall 20192019-08-09T16:58:48Z<p>Derman: /* 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 />
|<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=17606Algebra and Algebraic Geometry Seminar Spring 20202019-08-02T12:05:03Z<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=17605Algebra and Algebraic Geometry Seminar Spring 20202019-08-02T12:04:51Z<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 />
| Reserved (Matroids Day)<br />
|-<br />
|}</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2020&diff=17604Algebra and Algebraic Geometry Seminar Spring 20202019-08-02T11:57:59Z<p>Derman: Created page with "== Spring 2020 Schedule == {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title !align="left" | host(s) |- |February 7 |Jonathan Monta&#241;..."</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 />
|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 />
|<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 />
|}</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=17594Algebra and Algebraic Geometry Seminar Fall 20192019-07-30T21:59:57Z<p>Derman: /* 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 />
|<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 />
|<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17290Algebra and Algebraic Geometry Seminar Spring 20192019-04-08T14:12:27Z<p>Derman: /* 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 />
|Symbolic Powers and the (Stable) Containment Problem<br />
|Daniel<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.<br />
<br />
===Elo&iacute;sa Grifo===<br />
'''Symbolic powers and the (stable) containment problem'''<br />
<br />
Given a variety X in C^d, corresponding to an ideal I, which polynomials vanish up to order n along X? The polynomials in the n-th symbolic power of I, which are often not the same as the polynomials in the n-th ordinary power of I.<br />
<br />
In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by Ein--Lazersfeld--Smith, Hochster--Huneke and Ma--Schwede could be improved. Harbourne's Conjecture is a statement depending on n that unfortunately has been disproved for particular values of n. However, recent evidence points towards a stable version of Harbourne's conjecture, where we substitute all n by all n large enough. Some of that evidence is joint work with Craig Huneke and Vivek Mukundan.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17289Algebra and Algebraic Geometry Seminar Spring 20192019-04-08T14:11:57Z<p>Derman: /* Botong 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 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.<br />
<br />
===Elo&iacute;sa Grifo===<br />
'''Symbolic powers and the (stable) containment problem'''<br />
<br />
Given a variety X in C^d, corresponding to an ideal I, which polynomials vanish up to order n along X? The polynomials in the n-th symbolic power of I, which are often not the same as the polynomials in the n-th ordinary power of I.<br />
<br />
In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by Ein--Lazersfeld--Smith, Hochster--Huneke and Ma--Schwede could be improved. Harbourne's Conjecture is a statement depending on n that unfortunately has been disproved for particular values of n. However, recent evidence points towards a stable version of Harbourne's conjecture, where we substitute all n by all n large enough. Some of that evidence is joint work with Craig Huneke and Vivek Mukundan.</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17143Algebra and Algebraic Geometry Seminar Spring 20192019-03-12T12:04:13Z<p>Derman: /* 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 />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<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 />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17142Algebra and Algebraic Geometry Seminar Spring 20192019-03-12T12:03:21Z<p>Derman: /* 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 />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|http://www.math.tamu.edu/~ola/ Alexsandra Sobieska (Texas A&ampM)<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17112Algebra and Algebraic Geometry Seminar Spring 20192019-03-05T22:21:13Z<p>Derman: /* 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 />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17080Colloquia2019-03-01T23:30:16Z<p>Derman: /* Vladimir Sverak */</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 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[#Angelica Cueto (The Ohio State University)| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) <br />
|[[# Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| On the degrees and complexity of algebraic varieties ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 22 '''Monday'''<br />
| [https://justinh.su Justin Hsu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| Lempp<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: 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 />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: 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 />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
===Vladimir Sverak===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
<br />
===Jason McCullough===<br />
<br />
Title: On the degrees and complexity of algebraic varieties<br />
<br />
Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17079Colloquia2019-03-01T23:29:48Z<p>Derman: /* Spring 2019 */</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 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[#Angelica Cueto (The Ohio State University)| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) <br />
|[[# Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| On the degrees and complexity of algebraic varieties ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 22 '''Monday'''<br />
| [https://justinh.su Justin Hsu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| Lempp<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: 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 />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: 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 />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
===Vladimir Sverak===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17044Algebra and Algebraic Geometry Seminar Spring 20192019-02-27T01:21:05Z<p>Derman: /* Chris Eur */</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 />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17043Algebra and Algebraic Geometry Seminar Spring 20192019-02-27T01:20:37Z<p>Derman: /* 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 />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17035Algebra and Algebraic Geometry Seminar Spring 20192019-02-25T03:28:14Z<p>Derman: /* Michael Brown */</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 />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=17034Algebra and Algebraic Geometry Seminar Spring 20192019-02-25T03:27:40Z<p>Derman: /* 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 />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=16928Colloquia2019-02-15T15:53:41Z<p>Derman: /* Angelica Cueto (The Ohio State University) */</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 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# Angelica Cueto| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: 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 />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: 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 />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=16927Colloquia2019-02-15T15:32:42Z<p>Derman: /* Lillian Pierce (Duke University) */</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 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# Angelica Cueto| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: 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 />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement "any smooth surface of degree three in P^3 contains exactly 27 lines'' is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: 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 />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=16926Colloquia2019-02-15T15:32:15Z<p>Derman: /* Spring 2019 */</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 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# Angelica Cueto| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| Maksym Radziwill (Caltech)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: 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 />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: 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 />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<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>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16850Algebra and Algebraic Geometry Seminar Spring 20192019-02-06T20:38:11Z<p>Derman: /* 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 />
|TBD<br />
|Daniel<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|Shamgar Gurevich??<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16849Algebra and Algebraic Geometry Seminar Spring 20192019-02-06T20:37:35Z<p>Derman: /* 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 />
|Chris Eur (Berkeley)<br />
|TBD<br />
|Local<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|Shamgar Gurevich(??)<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16848Algebra and Algebraic Geometry Seminar Spring 20192019-02-06T20:37:20Z<p>Derman: /* 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 />
|Chris Eur (Berkeley)<br />
|TBD<br />
|Local<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|[http://www-personal.umich.edu/~ecanton/ Eric Canton (Michigan)]<br />
|TBD<br />
|Michael<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 />
===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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16702Algebra and Algebraic Geometry Seminar Spring 20192019-01-24T12:03:01Z<p>Derman: /* Isabel Vogt */</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<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 />
|TBD<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 />
|Shamgar Gurevich (Wisconsin)<br />
|Harmonic Analysis on GLn over finite fields, and Random Walks<br />
|Local<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|TBD<br />
|TBD<br />
|TBD<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 />
<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).</div>Dermanhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2019&diff=16701Algebra and Algebraic Geometry Seminar Spring 20192019-01-24T12:02:28Z<p>Derman: /* 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<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 />
|TBD<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 />
|Shamgar Gurevich (Wisconsin)<br />
|Harmonic Analysis on GLn over finite fields, and Random Walks<br />
|Local<br />
|-<br />
|March 8<br />
|Jay Kopper (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|March 15<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|March 22<br />
|No Meeting<br />
|Spring Break<br />
|TBD<br />
|-<br />
|March 29<br />
|[https://math.berkeley.edu/~ceur/ Chris Eur (UC Berkeley)]<br />
|TBD<br />
|Daniel<br />
|-<br />
|April 5<br />
|TBD<br />
|TBD<br />
|TBD<br />
|-<br />
|April 12<br />
|TBD<br />
|TBD<br />
|TBD<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.</div>Derman