# MSCS Seminar Calendar

Monday September 25, 2017

**Graduate Infinity Categories Seminar**

Infinity Categories: Examples and Applications

Gregory Taylor (UIC)

10:00 AM in SEO 1227

We explore the utility of infinity categories in various areas of mathematics. Topics (may) include (but are not limited to) TQFTs and the Cobordism Hypothesis, locally constant sheaves, and (Derived) Algebraic Geometry.

**Analysis and Applied Mathematics Seminar**

Explosion in stochastic cascades and well-posedness for the 3D Navier-Stokes equations

Radu Dascaliuc (Oregon State University)

4:00 PM in SEO 636

The idea of re-casting existence and uniqueness for a mild formulation of the Navier-Stokes equations in terms of multiplicative stochastic processes (cascades) goes back to Le Jan and Sznitman work in the 1990’s. In this talk I will address these cascades in the scaling-invariant setting, showing that the process develops infinitely many branches in finite time — a phenomenon called explosion. In previous work, explosion presented an obstacle in establishing uniqueness of the solutions. Nevertheless, we can show that both existence and uniqueness hold for small initial data. I will conclude by discussing possible implications of explosion to the problem of uniqueness of the solutions with large initial data.

Tuesday September 26, 2017

**Logic Seminar**

Variations of the stick principle

William Chen (Ben-Gurion University)

4:00 PM in SEO 427

The stick principle is a weakening of Jensen's diamond that asserts that there is a family of infinite subsets of $omega_1$ so that any uncountable subset of $\omega_1$ has some member of the family as a subset. We will give a forcing construction to separate versions of the stick principle which put a bound on the order-type of the subsets in the family. Many open problems remain about the relationship between different variations of this principle, such as the existence of certain club-guessing sequences or Suslin trees, and we will describe some progress in this direction.

Wednesday September 27, 2017

**Algebraic K-Theory Seminar**

Chern characters of perfect modules over curved algebras

Michael Brown (UW-Madison)

10:30 AM in SEO 1227

This is a report on joint work with Mark Walker. Let k be a field of characteristic 0, and let A be a smooth, essentially finite type k-algebra. The classical Hochschild-Kostant-Rosenberg isomorphism identifies the periodic cyclic homology of A with its de Rham cohomology. Moreover, classical Chern-Weil theory provides an explicit formula for the Chern character of a projective A-module in terms of this identification. The goal of this project is to generalize this story to the setting of "curved algebras", i.e. graded k-algebras equipped with a specified degree 2 element. In this talk, I will recall a well-known generalization of the HKR theorem to the setting of curved algebras, and I will discuss a Chern-Weil-type formula for the Chern character of perfect modules over curved algebras satisfying an appropriate smoothness condition.

**Statistics Seminar**

Weighted limit theorems and applications

Yanghui Liu (Purdue University)

4:00 PM in SEO 636

The term “limit theorem” is associated with a multitude of statements having to do with the convergence of probability distributions of sums of increasing number of random variables. Given that a limit theorem result holds, “weighted limit theorem” considers the asymptotic behavior of the corresponding weighted sums. The weighted limit theorem problem has drawn a lot of attention in recent articles due to its key role in topics such as parameter estimations, Ito’s formula in law, time-discrete numerical schemes, and normal approximations, and various “unexpected” weighted limit theorems have been discovered since then. The purpose of this talk is to introduce a general framework and a transferring principle for this problem, and to provide improvement of the existing results in a few aspects.

Thursday September 28, 2017

**Louise Hay Logic Seminar**

VC Dimension, VC Density, and the Sauer-Shelah Dichotomy - Part II

Roland Walker (UIC)

1:00 PM in SEO 427

Vapnik-Chervonenkis dimension and density are two measures of combinatorial complexity which arose from the study of probability theory. During this two-part talk, we will discuss these measures and their duals both in the classical and model-theoretic contexts, prove the famous Sauer-Shelah Lemma, discuss the relationship between VC dimension and NIP, and time permitting discuss some recent applications and open questions.

Friday September 29, 2017

**Departmental Colloquium**

Kahler-Einstein metrics

Gabor Szekelyhidi (University of Notre Dame)

3:00 PM in SEO 636

Kahler-Einstein metrics are of fundamental importance in
Kahler geometry, with connections to algebraic geometry, geometric
analysis, string theory amongst other fields. Their study has received
a great deal of attention recently, culminating in the solution of the
Yau-Tian-Donaldson conjecture, characterizing which complex manifolds
admit Kahler-Einstein metrics. I will give an overview of the field,
including some recent developments.

Wednesday October 4, 2017

**Statistics Seminar**

Joint Estimation of Fractal Indices for Bivariate Gaussian Processes

Yimin Xiao (MSU)

4:00 PM in SEO 636

Multivariate (or vector-valued) stochastic processes are important in probability, statistics and various scientific areas as stochastic models. In recent years, there has been increasing interest in investigating their statistical inference and prediction.
In this talk, we study the problem for estimating jointly the fractal indices of a bivariate Gaussian process. These indices not only determine the smoothness of each component process, fractal behavior of the whole process, but also play important roles in characterizing the dependence structure among the components.
Under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators for bivariate fractal indices. Our main results show the effect of the cross dependence structure on the performance of the estimators.
This is a joint paper with Yuzhen Zhou.

Friday October 6, 2017

**Departmental Colloquium**

Images, PDEs and hierarchical construction of solutions with critical regularity

Eitan Tadmor (University of Maryland)

3:00 PM in SEO 636

Edges are noticeable features in images which can be extracted from noisy data using different variational
models. The analysis of such models leads to the question of representing general L^2-data as the
divergence of uniformly bounded vector fields.
We use a multi-scale approach to construct uniformly bounded solutions of div U=f for
general f’s in the critical regularity space L^2(T^2). The study of this equation and related
problems was motivated by recent results of Bourgain & Brezis. The intriguing critical aspect
here is that although the problems are linear, construction of their solution is not. These
constructions are special cases of a rather general framework for solving linear equations in
representations U=\sum_j u_j which we introduced earlier in the context of image processing,
yielding a multi-scale decomposition of "image" U.

Tuesday October 10, 2017

**Logic Seminar**

Borel Complexity and the Schroder-Bernstein Property

Douglas Ulrich (Maryland)

4:00 PM in SEO 427

Borel Complexity and the Schroder-Bernstein Property
I describe some new techniques for proving non-Borel reducibility results, and give some applications, including: suppose the collection of countable models of a sentence sigma of L_{omega_1 omega} satisfies the Schroder-Bernstein property, that is, if two countable models are bi-embeddable then they are isomorphic. Then, assuming a mild large cardinal, sigma is not Borel complete.

We meet for lunch at noon on the first floor of SEO.

Friday October 13, 2017

Monday October 16, 2017

**Statistics Seminar**

Data Science 2.0

Dan Spillane (IBM)

4:00 PM in SEO 636

What's the purpose of Data Science anyway? In this discussion we'll explore how we need to turn data science upside-down to create the real value of this powerful trade. We need to push desired (business, social, economic...) outcomes to the forefront (the hypothesis) and leverage data, data platforms and AI to develop the questions we don't even know to ask and then help answer. We need to be data pioneers not just data engineers. Looking forward to a fruitful and living dialogue on Data Science 2.0.

Monday October 23, 2017

**Mathematics Computer Science Seminar**

Graph Pressing Sequences and Binary Linear Algebra

Joshua Cooper (University of South Carolina)

10:00 AM in SEO 612

One can construct a useful metric on genome sequences by computing minimal-length sortings of (signed) permutations by reversals. Hannenhalli and Pevzner famously showed that such sorting sequences are essentially equivalent to a certain sequences of operations -- ``vertex pressing'' -- on bicolored (aka loopy) graphs. We examine the matrix algebra over GF(2) that arises from the theory of such sequences, providing a collection of equivalent conditions for their existence and showing how linear algebra, poset theory, and group theory can be used to study them. We discuss enumeration, characterization, and recognition of uniquely pressable graphs (those with exactly one pressing sequence); a relation on pressing sequences that has a surprisingly diverse set of characterizations; and some open problems.

Please note the unusual time and room.

**Geometry, Topology and Dynamics Seminar**

Translation-like actions of nilpotent groups

Mark Pengitore (Purdue University)

3:00 PM in SEO 636

Whyte introduced translation-like actions of groups which serve as geometric generalization of subgroup containment. He then proved a geometric reformulation of the von Neumann conjecture by demonstrating a finitely generated group is nonamenable if and only if it admits a translation-like action by a non-abelian free group. This provides motivation for the study of what groups can translation-like on other groups. As a consequence of Gromov's polynomial growth theorem, only nilpotent groups can act translation-like on other nilpotent groups. In joint work with David Cohen, we demonstrate if two nilpotent groups have the same growth, but non-isomorphic Carnot completions, then they can't act translation-like on each other.

Wednesday October 25, 2017

**Algebraic Geometry Seminar**

Frobenius twists of ample vector bundles

Daniel Litt (Columbia University)

4:00 PM in SEO 427

In 1987, Deligne and Illusie famously gave an algebraic proof of the degeneration of the Hodge-to-de Rham spectral sequence and the Kodaira vanishing theorem. Their methods have been used since (by Arapura and others) to prove strong vanishing theorems. I'll discuss their methods, a conjecture that would strengthen them, and a proof of some important special cases of that conjecture. I'll also give some applications to toric varieties.

Friday October 27, 2017

Monday October 30, 2017

Wednesday November 1, 2017

Friday November 3, 2017

Monday November 6, 2017

**Algebraic Geometry Seminar**

The space of equations for a curve of prescribed gonality

Dhruv Ranganathan (MIT)

4:00 PM in SEO 427

The Brill-Noether varieties of a curve C parameterize embeddings of C of prescribed degree into a projective space of prescribed dimension, i.e. equations for the curve. When C is general, these varieties are well understood: they are smooth, irreducible, and have the "expected" dimension. As one ventures deeper into the moduli space, past the general curve, these varieties exhibit intricate, even pathological, behaviour: they can be highly singular and their dimensions are unknown. A first measure of the failure of a curve to be general is its gonality. Based on an analogous combinatorial problem on graphs, Pflueger conjectured a formula for the dimensions of the Brill-Noether varieties for general curves of a given gonality. I will present joint work with Dave Jensen, in which we prove Pflueger’s conjecture. The proof blends non-archimedean analytic techniques, ideas from logarithmic Gromov-Witten theory, and the geometry of scrolls.

Monday November 13, 2017

Wednesday November 15, 2017

**Algebraic Geometry Seminar**

Dominating varieties by liftable ones

Remy van Dobben de Bruyn (Columbia University)

4:00 PM in SEO 427

Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

Monday November 20, 2017

Wednesday November 22, 2017

Wednesday November 29, 2017

Monday December 4, 2017

Wednesday December 6, 2017

Friday February 16, 2018

Friday March 9, 2018

Friday March 23, 2018

Wednesday April 25, 2018