# 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.

**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.

Friday March 31, 2017

Monday April 3, 2017

Wednesday April 5, 2017

Friday April 7, 2017

Monday April 10, 2017

Wednesday April 12, 2017

Thursday April 13, 2017

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

Wednesday April 26, 2017

Friday April 28, 2017