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# MSCS Seminar Calendar

Monday December 2, 2013
Special Colloquium
Out-of-equilibrium dynamics of nonlinear dispersive equations: From energy cascades to weak turbulence
Zaher Hani (Courant Institute, NYU)
3:00 PM in SEO 636
Out-of-equilibrium dynamics are a characteristic feature of the long-time behavior of nonlinear dispersive equations (PDEs) on bounded domains. Energy cascades and weak (or wave) turbulence are main aspects of such out-of-equilibrium dynamics. In this talk, we will start by explaining what all those concepts mean, why they arise, and the mathematical problems involved in studying them. Afterwards, we will describe two main approaches that were adopted (in the mathematics and physics communities) to capture these phenomena. The first approach is based on a relation between energy cascades and the growth of Sobolev norms of solutions. The second is based on deriving "effective equations" for the dynamics by taking various limits of the original system (this is the guiding philosophy of weak turbulence theory). We will report on some recent progress on both approaches.

The Simple Continued Fraction for $e$
Charles Alley (UIC)
3:00 PM in SEO 427
In this talk I will give results from my bachelor's thesis. Specifically, I will make explicit connections between linear fractional transformations and continued fractions. Then, using the language of linear algebra, I will prove some basic results which can then be applied to derive the simple continued fraction for $e = [2,1,2,1,1,4,1,1,6,1,\cdots]$.

Applied Mathematics Seminar
N/A
N/A (No seminar)
4:00 PM in SEO 636

Chaos and perturbations in nonlinear systems
Marc Kjerland (UIC)
4:30 PM in SEO 636
Most problems in contemporary science are nonlinear and often display sensitivity to initial conditions or multiscale structure. Due to these difficulties, alternative notions of "solution" must be considered. I will present some concepts from nonlinear dynamics, including chaos and perturbation response, as well as applications to problems in the mathematical geosciences.
Tuesday December 3, 2013
Number Theory Seminar
A Multiple Dirichlet Series Associated to Binary Quadratic Forms
Li-Mei Lim (Boston College)
1:00 PM in SEO 636
It is well-known that the sum of special values of the $GL(2)$ Eisenstein series is equal to (up to some factors) $\zeta(s)L(s,\chi_d)$, where $\zeta(s)$ is the Riemann zeta function and $L(s, \chi_d)$ is the quadratic Dirichlet $L$-series. In this talk, I will describe a new proof for this old result, using a multiple Dirichlet series associated to binary quadratic forms. In addition, I will describe generalizations and extensions.

Quantum Topology / Hopf Algebra Seminar
Rasmussen Invariant
Lou Kauffman (UIC)
3:00 PM in SEO 612
This talk outlines the Rasmussen invariant and begins working on the details.

Logic Seminar
Computability in the class of real closed fields
Victor Ocasio (Notre Dame)
4:00 PM in SEO 427
The class of Real Closed Fields (RCF) is known to have very nice model theoretic properties, among them o-minimality and quantifier elimination. In our work, we consider some non- elementary subclasses of RCF and explore their computability theoretic properties. We locate the class of Archimedean Real Closed Fields using Turing computable embeddings (an analog of Borel embeddings) and compare it with other non-elementary first order subclasses of RCF. We also explore relative categoricity and show that under some conditions one can obtain a sharp result on the complexity of the relative categoricity of a real closed field that is constructed using a linear order as an oracle.
Wednesday December 4, 2013
Special Colloquium
Character rigidity for lattices in higher-rank groups
Jesse D. Peterson (Vanderbilt University)
3:00 PM in SEO 636
A character on a group is a class function of positive type. For finite groups, the classification of characters is closely related to the representation theory of the group and plays a key role in the classification of finite simple groups. Based on the rigidity results of Mostow, Margulis, and Zimmer, it was conjectured by Connes that for lattices in higher rank Lie groups the space of characters should be completely determined by the finite dimensional representations of the lattice. In this talk, I will give an introduction to this conjecture (which has now been solved in a number of cases), and I will discuss its relationship to ergodic theory, abstract harmonic analysis, invariant random subgroups, and von Neumann algebras.
Thursday December 5, 2013
Quantum Topology / Hopf Algebra Seminar
Rasmussen Invariant
Lou Kauffman (UIC)
3:00 PM in SEO 612
This talk continues Tuesday's talk.

Louise Hay Logic Seminar
Complete left-invariant metrics for automorphism groups of models
Sam Ziegler (UIC)
4:00 PM in SEO 427
Any Polish group can be equipped with a compatible left-invariant metric; however, there may be no compatible left-invariant metric which is also complete. Groups which do have such a metric are known as CLI groups. In this talk, we will examine a theorem, due to Gao, characterizing when groups of the form $Aut(\mathcal{M})$ are CLI. It turns out that for such automorphism groups, CLI can be reformulated as a property of the Scott sentence of $\mathcal{M}$.
Friday December 6, 2013
Special Colloquium
L^p bounds for eigenfunctions on locally symmetric spaces
Simon L. Marshall (Northwestern University)
3:00 PM in SEO 636
Abstract: There is a classical theorem of Sogge that provides bounds for the L^p norms of a Laplace eigenfunction on a compact Riemannian manifold, that are sharp on the sphere and for spectral clusters. I will present a generalization of this theorem to eigenfunctions of the full ring of invariant differential operators on a locally symmetric space, as well as a theorem on the restriction of eigenfunctions to maximal flat subspaces. Time permitting, I will discuss ways in which these bounds can be improved using inputs from number theory.
Tuesday December 10, 2013
Logic Seminar
Title: Characterizing successor cardinals by $L_{\omega_1,\omega}$-sentences.
Ioannis Souldatis (University of Detroit Mercy)
3:30 PM in SEO 427
An $L_{\omega_1,\omega}$ sentence $\phi$ characterizes a cardinal $\kappa$, if $\phi$ has models in all powers up to $\kappa$, but not in $\kappa^+$. During the talk we will focus on the results and the construction in Hjorth's [1], and state some extensions of these results, as well as questions that remain open.
[1] Hjorth, G. Knight's model, its automorphism group, and characterizing the uncountable cardinals J. Math. Log., 2002, 2, 113-144
Friday December 13, 2013
Elementary recursive bounds for Hilbert 17th problem
Marie-Francoise Roy (University of Rennes I)
1:00 PM in SEO 1227
Monday January 13, 2014
Special Colloquium
TBA
Elena D. Fuchs (University of California, Berkeley)
3:00 PM in SEO 636

Applied Mathematics Seminar
N/A
No seminar
4:00 PM in SEO 636
Wednesday January 15, 2014
Special Colloquium
TBA
Jeffrey Danciger (University of Texas, Austin)
3:00 PM in SEO 636

Algebraic Geometry Seminar
TBA
Tiankai Liu (MIT)
4:00 PM in SEO 427
Friday January 17, 2014
Special Colloquium
TBA
Antonio C. Auffinger (University of Chicago)
3:00 PM in SEO 636
Wednesday January 22, 2014
Statistics Seminar
TBA
Shuwen Lou (University of Washington)
4:00 PM in SEO 636
Friday January 24, 2014
Special Colloquium
TBA
TBA
3:00 PM in SEO 636
Monday January 27, 2014
Geometry, Topology and Dynamics Seminar
Classification of solenoids
Olga Lukina (UIC)
3:00 PM in SEO 636
Matchbox manifolds are foliated spaces whose transversal spaces are totally disconnected. In this work, we show that the local dynamics of a certain class of minimal matchbox manifolds classify their total space, up to homeomorphism. A key point is the use Alexandroff's notion of a Y-like continuum, where Y is an aspherical closed manifold which satisfies the Borel Conjecture. In particular, we show that two equicontinuous $T^n$-like matchbox manifolds of the same dimension, are homeomorphic if and only if their corresponding restricted pseudogroups are return equivalent. With an additional geometric assumption, our results apply to Y-like weak solenoids where Y satisfies these conditions. At the same time, we show that these results cannot be extended to include classes of matchbox manifolds fibering over a closed surface of genus 2 manifold which we call "adic-surfaces". These are 2-dimensional matchbox manifolds that have structure induced from classical 1-dimensional Vietoris solenoids. We also formulate conjectures about a generalized form of the Borel Conjecture for minimal matchbox manifolds.

Applied Mathematics Seminar
Fokas Integral Equations for Layered Media Scattering
Dave Nicholls (UIC)
4:00 PM in SEO 636
Wednesday February 5, 2014
Combinatorics Seminar
TBA
Ameerah Chowdhuri (Carnegie-Mellon)
3:00 PM in SEO 427
Monday February 10, 2014
Applied Mathematics Seminar
Solutions of some Monge-Ampere equations with degeneracy or singularities
Tianling Jin (University of Chicago)
4:00 PM in SEO 636
Wednesday February 19, 2014
Algebraic Geometry Seminar
TBA
Brendan Hassett (Rice University)
4:00 PM in SEO 427
Friday February 21, 2014
Departmental Colloquium
TBA
Brendan Hassett (Rice University)
3:00 PM in SEO 636
Wednesday February 26, 2014
Algebraic Geometry Seminar
TBA
Zhiyu Tian (Caltech)
4:00 PM in SEO 427
TBA
Wednesday March 5, 2014
Distinguished Lecture Series
TBA
Mike Hopkins (Harvard University)
3:00 PM in TBA

Algebraic Geometry Seminar
TBA
Colleen Robles (Texas A&M)
4:00 PM in SEO 427
Thursday March 6, 2014
Distinguished Lecture Series
TBA
Mike Hopkins (Harvard University)
3:00 PM in TBA
Friday March 7, 2014
Distinguished Lecture Series
TBA
Mike Hopkins (Harvard University)
3:00 PM in TBA
Wednesday March 12, 2014
Algebraic Geometry Seminar
TBA
Yaim Cooper (Harvard University)
4:00 PM in SEO 427
TBA
Wednesday March 19, 2014
Algebraic Geometry Seminar
TBA
Zsolt Patakfalvi (Princeton University)
4:00 PM in SEO 427
TBA
Friday March 21, 2014
Departmental Colloquium
TBA
Rakesh Vohra (University of Pennsylvania)
3:00 PM in SEO 636
Wednesday April 9, 2014
Statistics Seminar
TBA
Paul Livermore Auer (University of Wisconsin at Milwaukee)
4:00 PM in SEO 636
Monday April 21, 2014
Applied Mathematics Seminar
TBA
Maria Schonbek (University of California, Santa Cruz)
4:00 PM in SEO 636
Friday May 2, 2014
Departmental Colloquium
Atkin Memorial Lecture
Showu Zhang (Princeton University)
3:00 PM in TBA
The talk is followed by reception, dinner, and a workshop on Saturday and Sunday. Details to follow.