Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, May 2, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, May 2, 2017

11:00 am in 345 Altgeld Hall,Tuesday, May 2, 2017

Parametrized Morse Theory, Cobordism Categories, and Positive Scalar Curvature

Nathan Perlmutter (Stanford)

Abstract: In this talk I will construct a cobordism category consisting of manifolds equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. I will identify the homotopy the of this cobordism category with the infinite loopspace of a certain Thom spectrum. Using the parametrized version of the Gromov-Lawson construction, I will then show how to use this cobordism category to probe the space of positive scalar curvature metrics on a closed, spin manifold of dimension > 4. Our main result detects many non-trivial homotopy groups in this space of positive scalar curvature metrics.

11:00 am in 241 Altgeld Hall,Tuesday, May 2, 2017

Introduction to p-adic modular forms and Hida families for GL(1)

Iván Blanco-Chacón (University College Dublin)

Abstract: Part I of III on Hida Families, Hilbert Modular Forms and Arithmetic Applications. Part II and III (5/4 and 5/9) address Hilbert modular forms and a p-adic Gross-Zagier formula. Extended abstract at http://math.uiuc.edu/~duursma/HidaFamilies-IvanBC.html

12:00 pm in 243 Altgeld Hall,Tuesday, May 2, 2017

Convex cocompactness in finitely generated groups

Matthew Durham (Michigan Math)

Abstract: Stability is a strong quasiconvexity property which generalizes to finitely generated groups the classical notion of convex cocompactness from Kleinian groups, as well as the analogous notion in mapping class groups developed by Farb-Mosher, Kent-Leininger, and Hamenstädt.
In this talk, I will discuss what is currently known about stability, including various characterizes of stability and tools for identifying stable subgroups of important groups, such as mapping class groups, \(Out(F_n) \), and relatively hyperbolic groups. This talk involves joint work (in various combinations) with Tarik Aougab, Matthew Cordes, and Samuel Taylor.

2:00 pm in 347 Altgeld Hall,Tuesday, May 2, 2017

Random data Cauchy theory for power type nonlinear wave equations

Dana Mendelson (University of Chicago)

Abstract: In this talk, I will discuss the random data Cauchy theory for some power type nonlinear wave equations. Local well-posedness for these equations is by now well understood for initial data of subcritical or critical regularities, but techniques break down for initial data in the supercritical regime. In recent years, probabilistic methods have been used to investigate the behavior of solutions in regimes where deterministic techniques fail. I will present an almost sure global existence result in the supercritical regime for these equations, and a recent result on scattering for the energy critical equation in 4D with randomized radial data. I will discuss the main aspects of the proof, in particular, the randomization procedure for initial data in Sobolev spaces of low regularity, some new large deviation estimates, and energy estimates for a forced wave equation. This talk is based on several joint works with Jonas Luhrmann, and work with Ben Dodson and Jonas Luhrmann.

3:00 pm in 245 Altgeld Hall,Tuesday, May 2, 2017

Teaching to Transform: Addressing Race & Racism in the Classroom

Abstract: Teaching to Transform: Addressing Race & Racism in the Classroom will be held from 3-5 pm. All members of the Department of Mathematics are invited to attend.

3:00 pm in 241 Altgeld Hall,Tuesday, May 2, 2017

Infinite graph-Ramsey theory

Louis DeBiasio (Miami University)

Abstract: Ramsey's theorem guarantees a monochromatic copy of any countably infinite graph $G$ in any $r$-coloring of the edges of the complete graph $K_\mathbb{N}$. It is natural to wonder how "large" of a monochromatic copy of $G$ we can find with respect to some measure -- for instance, the (upper) density of the vertex set of $G$ in $\mathbb{N}$. Unlike finite graph-Ramsey theory, where this question has been studied extensively, the infinite version has been mostly overlooked. Erdős and Galvin proved that in every 2-coloring of $K_\mathbb{N}$, there exists a monochromatic path whose vertex set has upper density at least $2/3$, but it is not possible to do better than $8/9$. They also showed that there exists a monochromatic path $P$ such that for infinitely many $n$, the set $\{1,2,...,n\}$ contains the first $\frac{n}{3+\sqrt{3}}$ vertices of $P$, but it is not possible to do better than $2n/3$. We improve both results, in the former case achieving an upper density at least $3/4$ and in the latter case obtaining a tight bound of $2/3$. Inspired by this, we consider infinite analogs of well-known finite results on directed paths, trees (connected subgraphs), and graphs of bounded maximum degree/chromatic number. Joint work with Paul McKenney

4:00 pm in 131 English Building,Tuesday, May 2, 2017

Partial synchronization in dynamical systems

Lan Wang (UIUC Math)

Abstract: In nature, synchronization phenomena are ubiquitous. In this talk, we will focus on a specific type of partial synchronization. Basically, partial synchronization occurs due to two reasons: the inhomogeneity of oscillators and the inhomogeneity of coupling strength. For the first reason, a famous representative model is the Kuramoto Model. A sufficient condition of partial synchronization will be given for this model. For the second reason, we consider a slightly different model and analyze its partial synchronized state. Since this state is so fascinating and unexpected, it is specially named as "Chimera state". In the end, some open questions will be discussed. This talk should be approachable to all math graduate students.