# MSCS Seminar Calendar

Monday November 23, 2015

**Geometry, Topology and Dynamics Seminar**

Where does the Spin-Statistics Theorem come from?

Theo Johnson-Freyd (Northwestern University )

3:00 PM in SEO 636

The "spin-statistics theorem" is a physical phenomenon in which spinors --- (-1)-eigenstates of rotation by 360° --- are the same as fermions --- (-1)-eigenstates of switching two identical particles. Physicists usually understand this phenomenon as a fact about certain representations of the Lorentz group. In this talk I will give a very different mathematical "origin" of the spin-statistics theorem. I will explain that spin-statistics arises in precisely the same was as does the physical phenomenon of "unitarity", which in turn depends on a fundamental but nontrivial coincidence: the absolute Galois group of R happens to equal the group of connected components of the orthogonal group. This talk will assume no knowledge of physics.

**Combinatorics Seminar**

Point-curve incidences in the complex plane

Josh Zahl (MIT)

3:00 PM in SEO 427

The past few years have seen a flurry of new incidence results in the wake of Guth and Katz's seminal paper on the Erdős distinct distance problem. To date, most of these incidence theorems only apply to points and algebraic varieties in (real) Euclidean space. In many cases it is reasonable to expect that analogous theorems should hold over C, but limited progress has been made in this direction. In this talk, I will discuss a new point-curve incidence theorem in the complex plane. This is joint work with Adam Sheffer.

**Analysis and Applied Mathematics Seminar**

On Regularity Properties for Fluid Equations

Karen Zaya (UIC)

4:00 PM in SEO 636

Fundamental mathematical questions about the 3D Navier-Stokes remain unanswered, such as the question of the regularity of solutions to the equations. Thus it is natural to ask: If we assume a smooth solution to the 3D Navier-Stokes equations $u$ loses regularity at time $T^*$, what is the rate of blow-up? In this talk, we discuss blow-up rates of solutions in the homogeneous Sobolev spaces, in particular the new result in $\dot{H}^\frac{3}{2}$. We will also discuss a newly developed regularity criterion for the 3D Boussinesq equations, which only imposes a condition on the low modes of the velocity $u$. The key tool in the development of this weaker regularity criterion is linked to the dissipation wave number.

Tuesday November 24, 2015

**Quantum Topology / Hopf Algebra Seminar**

Kirby Calculus and Quantum Link Invariants

Louis H Kauffman (UIC)

3:00 PM in SEO 612

This is a self-contained, elementary talk about how quantum link invariants like the Jones polynomial can be
used to make topological invariants of three dimensional manifolds.

**Logic Seminar**

Infinite Time Turing Machines and Determinacy

Sherwood Hachtman (UIC)

4:00 PM in SEO 427

Infinite time Turing machines, introduced by Hamkins and Kidder, extend the usual notion of Turing computability by allowing the machine to proceed for an arbitrary ordinal number of steps. These machines may either halt or enter a loop at some countable ordinal stage; thus there are several feasible notions of "Turing jump" for infinite time Turing computability. I will discuss a recent result of Philip Welch illustrating an intimate connection between the jump operator identifying those computations which "eventually settle" (loop with fixed output), and $\Sigma^0_3$ determinacy.

Monday November 30, 2015

**Geometry, Topology and Dynamics Seminar**

The diameter of the $L^1$-metric on the group of area-preserving diffeomorphisms of $S^2$.

Egor Shelukhin (Institute for Advanced Study, Princeton)

3:00 PM in SEO 636

We use a geometric idea to give an analytic estimate for the word-length in the pure braid group
of $S^2$. This yields that the $L^1$-norm (and hence each $L^p$-norm, including $L^2$)
on the area-preserving diffeomorphism group of $S^2$ is unbounded.
This solves an open question arising from the work of Shnirelman and Eliashberg-Ratiu.
Joint work in progress with Michael Brandenbursky.

**Graduate Student Colloquium**

The p-adic Mandelbrot Set and Other Peculiarities of Arithmetic Dynamics

Cara Mullen (UIC)

4:00 PM in BH 209

The goal of this talk is to introduce the subject of p-adic dynamics: the study of dynamics over a field that is complete with respect to a nonarchimedean absolute value. We will discuss some of the major results, with a little motivation from classical complex dynamics. No previous knowledge of dynamical systems or number theory will be assumed.

Wednesday December 2, 2015

**Statistics Seminar**

Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise

Xia Chen (University of Tennessee)

4:00 PM in SEO 636

This work is concerned with the precise spatial asymptotic behavior for the parabolic Anderson equation
$$\frac{\partial u}{\partial t}(t,x)=\frac{1}{2}\triangle u(t,x)+V(t,x)u(t,x),\quad\quad\mathrm{with}\ u(0,x)=u_0(x),$$
where the homogeneous generalized Gaussian noise $V(t,x)$ is, among other forms, white or fractional white in time
and space. Associated with the Cole-Hopf solution to the KPZ equation, in particular, the precise asymptotic form
$$\lim_{R\to+\infty}(\log R)^{-2/3}\log\max_{|x|\leq R}\, u(t,x)=\frac{3}{4}\sqrt[3]{\frac{2t}{3}}\quad \mathrm{a.s.}$$
is obtained for the parabolic Anderson model $\partial_t u=\frac{1}{2}\partial^2_{xx}u+\dot{W}u$ with the $(1+1)$-white noise $\dot{W}(t,x)$.

Friday December 4, 2015

**Departmental Colloquium**

Numerical Simulation of Wave Propagation

David Nicholls (UIC)

3:00 PM in SEO 636

The interaction of waves (acoustic, electromagnetic, elastic) with layered
media plays an important role in many scientific problems. Among these are
seismic imaging, underwater acoustics, biosensing, and solar cells. The
ability to simulate scattered fields from these structures in a robust and
highly accurate fashion is of fundamental importance. In this talk we will
describe a class of rapid and highly accurate boundary perturbation schemes,
termed ``High--Order Perturbation of Surfaces'' (HOPS) Methods, for
delivering such numerical approximations. Time permitting we will describe
our efforts to not only detect layered media geometries based upon far--field
data, but also design these structures to have optimal scattering properties.

Tea at 4:15 PM in SEO 300

Tuesday December 8, 2015

**Quantum Topology / Hopf Algebra Seminar**

On infinitesimal bending

Ljubica S. Velimirovic (Faculty of Science and Mathematics, University of Nis, Serbia)

3:00 PM in SEO 612

We will consider infinitesimal bending problems related to change of geometric
magnitudes at Euclidean and Generalised Riemannian Space. Recent results of the author and cooperators Svetislav Mincic, Mica Stankovic, Marija Najdanovic, Milan Zlatanovic, Milica Cvetkovic and Nikola Velimirovic will be mentioned.

Monday December 14, 2015

Monday January 25, 2016

Monday February 1, 2016

Monday February 8, 2016

Tuesday February 9, 2016

Monday February 22, 2016

Friday February 26, 2016

Monday February 29, 2016

Monday March 14, 2016