# MSCS Seminar Calendar

Monday September 24, 2018

**Geometry, Topology and Dynamics Seminar**

Metric Contraction of the Cone Divisor by the Conical Kahler-Ricci Flow

Gregory Edwards (Notre Dame)

3:00 PM in 636 SEO

The conical Kahler-Ricci flow is a parabolic flow of Kahler metrics with cone singularities along a codimension one complex submanifold which deforms the smooth part of the metric by the Ricci curvature and keeps the conic boundary conditions fixed. On Hirzebruch surfaces, we analyze solutions of the flow with symmetry and show that the flow always reaches a finite time singularity which either contracts the cone divisor to a single point and the flow Gromov-Hausdorff converges to a projective orbifold, or the flow converges to either the Riemann sphere or a single point. This phenomenon fits into a conjectural framework that characterizes finite time non-collapsing singularities of the flow on complex surfaces.

**Analysis and Applied Mathematics Seminar**

Small Debye length limit for the Euler-Poisson system

Bongsuk Kwon (Ulsan National Institute for Science and Technology)

4:00 PM in 636 SEO

We discuss existence, time-asymptotic behavior, and quasi-neutral limit for the Euler-Poisson equations. Specifically, under the Bohm criterion, we construct the global-in-time solution near the stationary solution of plasma sheath, and also investigate its time-asymptotic behavior and small Debye length limit. If time permits, some key features of the proof and related problems will be discussed. This is joint work with C.-Y. Jung (UNIST) and M. Suzuki (Nagoya Tech.).

Tuesday September 25, 2018

**Graduate Groups and Dynamics Seminar**

Spectral gap and almost diophantine groups, I (after Benoist-De Saxcé)

Wouter van Limbeek (UIC)

3:00 PM in 1227 SEO

We say a group of matrices in a compact Lie group has spectral gap if the associated averaging operator has eigenvalues bounded away from 1. This property is a geometric analogue of the algebraic criterion of expansion in Cayley graphs, and is intimately connected with a number of interesting problems such as construction of expanders and behavior of random walks. In this talk, we discuss a result of Benoist-De Saxcé connecting the spectral gap property to diophantine properties of matrices, and establishing spectral gap for groups with algebraic entries. This is the first of a series of talks on this result.

**Logic Seminar**

A Homotopical View of Lascar Groups of First-Order Theories

Greg Cousins (Notre Dame)

3:30 PM in 427 SEO

In this talk, we will discuss how the Lascar group of a first-order theory, $T$, can be recovered as the fundamental group(-oid) of a certain space associated to the category of models, $\operatorname{Mod}(T)$. We will then discuss some examples illustrating how tools from algebraic topology can be used to compute the Lascar group of a theory. Time permitting, we will discuss generalizations to the context of AECs and questions their higher homotopy. No knowledge of homotopy theory will be assumed. This is joint work with Tim Campion and Jinhe Ye.

Wednesday September 26, 2018

**Mathematics Education Colloquium**

Assessing developmental education programs

Aida Alibek (UIC)

12:00 PM in 612 SEO

We will discuss the Goldwasser, Martin & Harris article "A Framework for Assessing Developmental Education Programs" in the context of developmental math.
Prior reading of the article is encouraged but not necessary. Everyone is welcome to attend.

**Graduate Algebraic Geometry Seminar**

Nef cones of Hilbert schemes of points on surfaces

Jay Kopper (UIC)

2:00 PM in 712 SEO

The Hilbert scheme of points parameterizes length $n$ zero-dimensional subschemes of a variety. A recent paper by Bolognese-Huizenga-Lin-Riedl-Schmidt-Woolf-Zhao computes the nef cone of these spaces. I will give an overview of their work, including necessary background on Hilbert schemes and nefness.

**Algebraic Geometry Seminar**

Uniform Approximation of Abhyankar Valuation Ideals in Prime Characteristic

Rankeya Datta (UIC)

4:00 PM in 427 SEO

We will prove a prime characteristic analogue of a result of Ein, Lazarsfeld and Smith on approximation of valuation ideals associated to real-valued Abhyankar (quasi-monomial) valuations.

**Statistics Seminar**

JMP and the Predictive Modeling Workflow

Kevin Potcner (JMP Statistical Discovery Software)

4:00 PM in 636 SEO

As the size and sources of data becomes more available in today's business environments, data analysts are beginning to add more sophisticated predictive statistical modeling techniques to their analysis toolkit.
A typical real-world predictive modeling workflow includes data cleaning and exploration, model fitting, model validation, model comparison, final model selection and deployment of the final predictive model.
In this presentation, a statistical scientist from JMP will illustrate the predictive modeling workflow by analyzing a real dataset. After data preparation and initial exploration, we will create a number of predictive models such as Multiple Linear Regression, Regression tree, Neural Net, and K-Nearest Neighbors.
We will evaluate each model and select the best model using the Prediction Profiler and JMP's Model Comparison tool.
Code will be automatically created in a variety of programming languages (e.g., SAS, SQL, Python, et al.) in order to implement that model in a production environment.

Friday September 28, 2018

**Departmental Colloquium**

Title: Common torsion points and a uniform Manin-Mumford bound for a family of genus 2 curves

Holly Krieger (University of Cambridge)

3:00 PM in 636 SEO

I will discuss joint work with Laura DeMarco and Hexi Ye in which we use dynamically-inspired techniques towards a conjecture of Bogomolov-Fu-Tschinkel asserting a uniform bound on the number of common torsion points of distinct elliptic curves. I will explain our strategy, which has general application to proving uniform bounds in unlikely intersections, and how this theorem implies a uniform bound on the number of torsion images in their Jacobians for a family of genus 2 curves. This talk will be accessible to a general mathematical audience.

Monday October 1, 2018

Wednesday October 3, 2018

**Algebraic Geometry Seminar**

Complex analytic compactifications of moduli spaces of Yang-Mills connections

Matei Toma (Nancy)

4:00 PM in 427 SEO

For a complex projective manifold (X,\omega) the Kobayashi-Hitchin correspondence gives homeomorphisms between moduli spaces of irreducible Hermitian-Yang-Mills connections and moduli spaces of stable vector bundles on X. A by now classical paper of Jun Li from 1993 shows that when X is two-dimensional this correspondence can be extended as a homeomorphism between natural compactifications of these moduli spaces existing on the gauge theoretical and on the algebraic geometric side, respectively. As a consequence one gets a complex analytic structure on the Donaldson-Uhlenbeck compactification of the moduli space of Hermitian-Yang-Mills connections on a fixed hermitian vector bundle on X. In this talk we present joint recent work together with Daniel Greb, Benjamin Sibley and Richard Wentworth extending these results to the higher dimensional situation.

Friday October 5, 2018

**Departmental Colloquium**

Sparse Polynomial Interpolation and Symmetric Tensor Decomposition

Lihong Zhi (ICERM)

3:00 PM in 636 SEO

The sparse interpolation problem has been studied and widely used in many different areas of science and engineering since the work of Prony (1795). Ankur Moitra in his paper at STOC 2015 has given an in-
depth analysis of how oversampling improves the conditioning of the arising Prony systems for sparse interpolation and signal recovery from numeric data. Moitra assumes that oversampling is done for a number of samples beyond the actual sparsity of the polynomial/signal. We give an algorithm that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation. Some recent work on computing the symmetric tensor rank by Prony's method will also be introduced.

**Geometry, Topology and Dynamics Seminar**

Pathology foliations and centralizer of diffeomorphisms

Disheng Xu (University of Chicago)

3:00 PM in 636 SEO

In 1990s, Shub and Wilkinson constructed a famous example of diffeomorphism f
with non-absolutely continuous invariant foliation W, i.e. there is a full Lebesgue volume set S which intersects each leaf of W on a zero leaf-measure set (or even a finite set).
In this talk we will show that Shub-Wilkinson example has virtually trivial centralizer,
i.e. for any g commutes with f, there exist non zero pair (k,l) such that f^k g^l=id.
This is a baby example of the joint work with D. Damjanovic and A. Wilkinson (in preparation).

Wednesday October 10, 2018

Friday October 12, 2018

Monday October 15, 2018

**Mathematical Computer Science Seminar**

List Coloring Cartesian Products of Graphs: Criticality and the List Color Function

Hemanshu Kaul (IIT)

3:00 PM in 427 SEO

The list chromatic number of the Cartesian product of graphs is not well understood. The best result is by Borowiecki, Jendrol, Kral, & Miskuf (2006) who proved that the list chromatic number of the Cartesian product of two graphs can be bounded in terms of the list chromatic number and the coloring number of the factors, implying a bound exponential in the list chromatic number of the factors.
We show how the knowledge of the list color function (list coloring analogue of the chromatic polynomial) can be applied to list coloring of Cartesian products. We introduce the notion of strongly chromatic choosable graphs, that includes odd cycles, cliques, many more infinite families of graphs, and the join of a clique with any other such graph, as a notion of color-criticality in the context of chromatic-choosability. This leads to improved bounds on choosability of Cartesian product of certain large classes of graphs and to classes of chromatic-choosable Cartesian products of graphs. This is joint work with Jeffrey Mudrock.

Monday October 29, 2018

Friday November 2, 2018

Monday November 5, 2018

Friday November 9, 2018

Monday November 12, 2018

Friday November 16, 2018

Monday November 19, 2018

Monday November 26, 2018

Friday November 30, 2018

Monday December 3, 2018

Wednesday January 23, 2019

Wednesday February 13, 2019

Friday March 1, 2019

Monday March 11, 2019

Wednesday March 13, 2019

Friday March 15, 2019

Wednesday March 27, 2019

Wednesday April 10, 2019

Wednesday April 17, 2019

Monday April 22, 2019