# MSCS Seminar Calendar

Monday March 27, 2017

**Combinatorics Seminar**

A variation of the Ramsey problem: (p,q)-colorings

Alex Cameron (UIC)

2:00 PM in SEO 612

For fixed integers $p$ and $q$, let $f(n,p,q)$ denote the minimum number of colors needed to color all of the edges of the complete graph $K_n$ such that no clique of $p$ vertices spans fewer than $q$ distinct colors. Any edge-coloring with this property is known as a $(p,q)$-coloring. In this talk I will present a recent result showing that $f(n,5,5) \leq n^{1/3 + o(1)}$ as $n \rightarrow \infty$ by giving an explicit $(5,5)$-coloring. This improves upon the best known probabilistic upper bound of $O\left(n^{1/2}\right)$ given by Erdos and Gyarfas, and comes close to matching the best known lower bound $\Omega\left(n^{1/3}\right)$.

**Geometry, Topology and Dynamics Seminar**

Friedlander-Milnor's problem for diffeomorphism groups

Sam Nariman (Northwestern University)

3:00 PM in SEO 636

Let G be a finite dimensional Lie group and G^delta be the same group with discrete topology. The natural homomorphism from G^delta to G induces a continuous map from BG^delta to BG. Milnor conjectured that this map induces a p-adic equivalence. In this talk, we discuss the same map for infinite dimensional Lie groups, in particular for diffeomorphism groups and symplectomorphisms. In these cases, we show that the map from BG^delta to BG induces split surjection on cohomology with finite coefficients in "the stable range". If time permits, I will discuss applications of these results in foliation theory, in particular flat surface bundles.

**Analysis and Applied Mathematics Seminar**

Invariant manifolds for supercritical KDV equation

Zhiwu Lin (Georgia Institute of Technology)

4:00 PM in SEO 636

Consider
generalized KDV equations with a power non-linearity (u^p)_x. These KDV
equations have solitary traveling waves, which are linearly unstable
when p>5 (supercritical case). Jointly with Jiayin Jin and Chongchun
Zeng, we constructed invariant manifolds (stable, unstable and center)
near the orbit of the unstable traveling waves in the energy space. In
particular, the local uniqueness and orbital stability of the center
manifold is obtained. These invariant manifolds give a complete
description of the dynamics near unstable traveling waves.

Tuesday March 28, 2017

**Quantum Topology / Hopf Algebra Seminar**

The Yokonuma--Hecke algebra and bt--algebra in Knot theory

Jesus Juyumaya (Instituto de Matematicas, Universidad de Valparaiso, Gran Bretana 1111, Valparaiso, Chile)

2:00 PM in SEO 612

I will show recent applications of the Yokonuma--Hecke algebra in the construction of new invariants for classical links; these invariants are constructed by using the Jones construction for the Homflypt polynomial (Jones recipe). Also, I will discuss the idea of framization of a knot algebra. Finally, I will show the construction of the so--called bt--algebra which is a knot algebra attached naturally to the Yokonuma--Hecke algebra.

**Commutative Algebra Seminar**

On Switala’s Matlis duality

Gennady Lyubeznik (University of Minnesota)

2:00 PM in SEO 427

N. Switala has developed a Matlis duality theory for D-modules. In this talk I am going to show how Switala's theory leads to a generalization of a recent result of R. Hartshorne and C. Polini on the structure of some local cohomology modules.

**Logic Seminar**

Stability and sparsity in sets of natural numbers

Gabriel Conant (Notre Dame )

4:00 PM in SEO 427

Stability and sparsity in sets of natural numbers
The additive group of integers is a well-studied example of a stable group, whose definable sets can be easily and explicitly described. However, until recently, very little has been known about stable expansions of this group. In this talk, we examine the relationship between model-theoretic stability of expansions of the form (Z,+,0,A), where A is a subset of the natural numbers, and the number theoretic behavior of A with respect to sumsets, asymptotic density, and arithmetic progressions.

Wednesday March 29, 2017

**Algebraic K-Theory Seminar**

Assembly maps for topological cyclic homology

Marco Varisco (SUNY-Albany)

1:00 PM in SEO 1227

Topological cyclic homology, a far-reaching generalization of Hochschild homology, is a powerful invariant of rings and plays an important role in algebraic K-theory. I will present joint work with Wolfgang Lück, Holger Reich, and John Rognes [arXiv:1607.03557], in which we use assembly maps to study the topological cyclic homology of group algebras. For any finite group G, for any connective ring spectrum A, and for any prime p, we prove that TC(A[G];p) is determined by TC(A[C];p) as C ranges over the cyclic subgroups of G. More precisely, we prove that for any finite group the assembly map with respect to the family of cyclic subgroups induces isomorphisms on all homotopy groups. For infinite groups, we establish pro-isomorphism, split injectivity, and rational injectivity results, as well as counterexamples to injectivity and surjectivity. In particular, for hyperbolic groups and for virtually finitely generated abelian groups, we show that the assembly map with respect to the family of virtually cyclic subgroups is split injective but in general not surjective---in contrast to what happens in algebraic K-theory.

**Phil Math Seminar**

The basic type structure underlying Martin-Löf type theory

William Howard (UIC)

3:00 PM in SEO 427

Univalent foundations employs an elaborate type structure whose
main ideas trace back to the basic type structure underlying Martin-Löf
type theory. I'll describe this basic type structure and how it arises
from an attempt to interpret Brouwer's intuitionistic mathematics by means
of a theory of constructions. No knowledge of this field, or of proof
theory, is assumed.

**Statistics Seminar**

Some statistical considerations in High-Throughput-Screening data evaluations in drug discovery

Dr. Viswanath Devanarayan (AbbVie)

4:00 PM in SEO 636

In High-Throughput-Screening efforts during the drug discovery process, hundreds of thousands of compounds are tested to identify promising drug candidates that modulate specific gene targets. These drug candidates may ultimately serve as therapeutic candidates for some disease indications of interest. Critical decisions related to compound selection and prioritization are made based on fairly limited data, and therefore rely greatly on data quality and reproducibility. Standard statistical metrics and methods in textbooks do not directly apply for these evaluations. This presentation will provide an overview of some statistical measures that were developed specifically for this application. The content of this presentation will be very practical and data-driven, and hence will be suitable for a broad audience.

**Algebraic Geometry Seminar**

Degenerations of Riemann surfaces together with a meromorphic differential

Samuel Grushevsky (Stonybrook)

4:00 PM in SEO 427

We describe a natural compactification of the moduli space of complex curves together with a meromorphic 1-form with prescribed multiplicities of zeroes and poles. Such a moduli space is the total space where the action of SL(2,R) is studied in Teichmuller dynamics, and is also the analog of the double ramification cycle on the moduli space of curves. Based on joint work with M. Bainbridge, D. Chen, Q. Gendron, M. Moeller.

Thursday March 30, 2017

**Quantum Topology / Hopf Algebra Seminar**

Motivations For Homotopy Type Theory - Part 2

Alexander Berenbeim (UIC)

2:00 PM in SEO 612

After last week's surfeit of abstract nonsense where we principally introduced Cartesian Closed Categories
(CCCs), briefly covered the \lambda-calculus, and made unfulfilling promises about (co)-monads,
comes a full reboot. We begin by emphasizing the main lesson which may have been obscured last week: models of the \lambda calculus are precisely CCCs and that the conversion rules correspond to introduction, elimination, and computation rules which are expressible as adjoints, which in turn give rise to (co)-monads. This lesson will be explicitly developed by closely working through the examples of the basic type formers found in ML Intuitionistic Type Theory and their interpretation in Homotopy Type Theory. We then will explicitly prove that $\pi_1(S^1) \cong Z$ by building
upon the machinery introduced in the first part of the talk. This talk should be interesting for those intrigued by univalent foundations, or who have an interest in learning more about formal proof verification. In particular, the second half of the talk will be an extended example in proving mathematical theorem in the Homotopy Type Theory fork of Coq. No background will be assumed.

Friday March 31, 2017

**Departmental Colloquium**

Model theory and Painleve equations

James Freitag (The University of Illinois at Chicago)

3:00 PM in SEO 636

Painleve equations are certain order two nonlinear differential equations which were isolated around the beginning of the last century by Painleve, Gambier, and Fuchs for reasons related to classical analytic problems. The equations arise in a variety of applications from physics to Diophantine geometry. In this talk, we will discuss how model theory can be used to resolve some open problems around the transcendence of Painleve equations.

**Geometry, Topology and Dynamics Seminar**

Mapping class groups and monodromy of some families of algebraic curves

Nick Salter (University of Chicago)

3:00 PM in SEO 636

Complex algebraic geometry is a wonderfully rich source of
geometric/topological phenomena. In this talk, I will survey some
connections between classical notions in algebraic geometry (e.g. smooth
algebraic curves in the projective plane) and low-dimensional topology,
particularly the mapping class group. The connection arises through the
notion of a “Riemann surface bundle”. A “family” of algebraic curves
arising via algebraic geometry naturally forms such a fiber bundle, and
any such bundle has a monodromy representation, i.e. a subgroup of the
mapping class group. These groups are rich and interesting, but currently
very poorly understood. I will discuss some work of mine in this direction
- one result constrains the size of these groups, and another shows they
are quite large in certain contexts. This will involve a blend of ideas
from algebraic geometry and the theory of the mapping class group,
particularly the Torelli group.

Tuesday April 4, 2017

**Number Theory Seminar**

The Breuil-Mézard conjecture when $l \ne p$

Jack Shotton (University of Chicago)

11:00 AM in SEO 612

Let $G={\rm Gal}(\overline{{\mathbb Q}}_p/{\mathbb Q}_p)$. The Breuil-Mézard conjecture relates the
complexity of deformation rings for mod $p$
Galois representations of $G$ with prescribed $p$-adic Hodge type to the reduction mod p of representations of
$GL_n({\mathbb Z}_p)$ associated to that type. It has been important in the $p$-adic Langlands program and in
first proof of
the Fontaine-Mazur conjecture for $GL_2$. We develop an analogous conjecture for mod l representations of $G$
when $l \ne p$, and explain how it can be proved with global methods.

Wednesday April 5, 2017

Friday April 7, 2017

Monday April 10, 2017

**Geometry, Topology and Dynamics Seminar**

Parabolic Higgs bundles and the Fourier-Mukai transform

Nathan Clement (Wisconsin )

3:00 PM in SEO 636

We work with some moduli spaces of (parabolic) Higgs bundles which come in infinite families indexed by rank. I'll give some motivation for the study of parabolic Higgs bundles, but the main problem will be to describe the moduli spaces. By applying some integral transforms, most importantly the Fourier-Mukai transform associated to the Poincare line bundle, we are able to reduce the rank of the problem and eventually get a good presentation of the moduli spaces. One fun technique involved in the argument deals with the spectrum of a one-parameter family of linear operators. When such an operator degenerates to one that is diagonalizable with repeated eigenvalues, the spectrum of the operator admits a scheme-theoretic refinement in a certain blowup which carries more information than simply the eigenvalues with multiplicity.

**Analysis and Applied Mathematics Seminar**

Nonlinear stability theory of self-gravitationg fluids

Juhi Jang (University of Southern California)

4:00 PM in SEO 636

I will review stability problems of Lane-Emden star configurations modeled by the Euler-Poisson system and present a recent joint work with Mahir Hadzic on the global-in-time existence of expanding stars in the mass-critical regime.

Wednesday April 12, 2017

Thursday April 13, 2017

**Algebraic Geometry Seminar**

Tautological classes on the moduli space of K3 surfaces

Rahul Pandharipande (ETH Zurich)

2:00 PM in SEO 427

I will discuss kappa classes on the moduli space of quasi-polarized
K3 surfaces and relations obtained from the moduli spaces of stable
maps to the universal family. I will explain the proof of the generation of
the tautological ring by Noether-Lefschetz loci. There are a number of
open questions. Joint work with Qizheng Yin.

Friday April 14, 2017

Monday April 17, 2017

**Analysis and Applied Mathematics Seminar**

Analysis of a feedback-control data assimilation algorithm

Cecilia Mondaini (Texas A&M University/ICERM)

4:00 PM in SEO 636

The purpose of this talk is to present some analysis results concerning a feedback-control (nudging) approach for data assimilation that works for a general class of dissipative dynamical systems and observables. First, I will consider the situation when the measurements are discrete in time and contaminated by systematic errors. In this case, we obtain an estimate for the error between the approximating solution and the reference solution that shows exponential convergence in time modulo the bound on the errors. Later, I will consider a numerical approximation of the nudging equation via the Postprocessing Galerkin Method, and show an analytical estimate of the truncation error committed in this finite-dimensional approximation. Most importantly, this error estimate is uniform in time. This is in contrast with the error estimate for the usual Galerkin approximation of the 2D Navier-Stokes equations, which grows exponentially in time. This talk is based on joint works with C. Foias and E. S. Titi.

Wednesday April 19, 2017

**Algebraic Geometry Seminar**

General hyperplane sections of 3-folds in positive characteristic

Kenta Sato (University of Tokyo)

4:00 PM in SEO 427

Since the Bertini theorem for free linear series fails in positive characteristic,
it is not clear whether a general hyperplane section of a klt 3-fold in positive characteristic has only klt singularities or not.
We give an affirmative answer when the characteristic is larger than 5.
This talk is based on joint work with Professor Shunsuke Takagi.

Friday April 21, 2017

Monday April 24, 2017

**Geometry, Topology and Dynamics Seminar**

On word hyperbolic surface bundles

Autumn Kent (University of Wisconsin)

3:00 PM in SEO 636

There is a characterization of hyperbolicity of the
fundamental group of a surface bundle due to Farb-Mosher-Hamenstaedt,
namely that the bundle has hyperbolic fundamental group if and only if the fundamental group of the base is ``convex cocompact,'' a notion analogous to
the synonymous notion in Kleinian groups. I will discuss joint work
with Bestvina, Bromberg, and Leininger that gives a new
characterization of convex cocompactness, namely that the group is
purely pseudo-Anosov and undistorted in the mapping class group.

Wednesday April 26, 2017

Friday April 28, 2017