Department of


Seminar Calendar
for events the day of Tuesday, November 19, 2019.

events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2019          November 2019          December 2019    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5                   1  2    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
 27 28 29 30 31         24 25 26 27 28 29 30   29 30 31            

Tuesday, November 19, 2019

11:00 am in 347 Altgeld Hall,Tuesday, November 19, 2019

Two theories of real cyclotomic spectra

Jay Shah

Abstract: The topological Hochschild homology $THH(R)$ constitutes a powerful and well-studied invariant of an associative ring $R$. As originally shown by Bokstedt, Hsiang and Madsen, $THH(R)$ admits the elaborate structure of a cyclotomic spectrum, whose formulation depends upon equivariant stable homotopy theory. More recently, inspired by considerations in p-adic Hodge theory, Nikolaus and Scholze demonstrated (under a bounded-below assumption) that the data of a cyclotomic spectrum is entirely captured by a system of circle-equivariant Frobenius maps, one for each prime p. They also give a formula for the topological cyclic homology $TC(R)$ directly from these maps. The purpose of this talk is to extend the work of Nikolaus and Scholze in order to accommodate the study of real topological Hochschild homology $THR$, which is a $C_2$-equivariant refinement of $THH$ defined for an associative ring with an anti-involution, or more generally an $E_\sigma$-algebra in $C_2$-spectra. The key idea is to make use of the $C_2$-parametrized Tate construction. This is joint work with J.D. Quigley and is based on the arXiv preprint 1909.03920.

1:00 pm in 347 Altgeld Hall,Tuesday, November 19, 2019

Global Strichartz estimates for the semiperiodic Schrodinger equation.

Alex Barron (illinois Math)

Abstract: We will discuss some recent results related to space-time estimates for solutions to the linear Schrodinger equation on manifolds which are products of tori and Euclidean space (e.g. a cylinder embedded in R^3 ). On these manifolds it is possible to prove certain analogues of the classical Euclidean Strichartz estimates which are scale-invariant and global-in-time. These estimates are strong enough to prove small-data scattering for solutions to the critical quintic NLS on R T and the critical cubic NLS on R^2 T (where T is the one-dimensional torus).

2:00 pm in 243 Altgeld Hall,Tuesday, November 19, 2019

An overview of Erdős-Rothschild problems and their rainbow variants

Lina Li (Illinois Math)

Abstract: In 1974, Erdős and Rothschild conjectured that the complete bipartite graph has the maximum number of two-edge-colorings without monochromatic triangles over all n-vertex graphs. Since then, a new class of colored extremal problems has been extensively studied by many researchers on various discrete structures, such as graphs, hypergraphs, Boolean lattices and sets.

In this talk, I will first give an overview of some previous results on this topic. The second half of this talk is to explore the rainbow variants of the Erdős-Rothschild problem. With Jozsef Balogh, we confirm conjectures of Benevides, Hoppen and Sampaio, and Hoppen, Lefmann, and Odermann, and completes the characterization of the extremal graphs for the edge-colorings without rainbow triangles. Next, we study a similar question on sum-free sets, where we describe the extremal configurations for integer colorings with forbidden rainbow sums. The latter is joint work with Yangyang Cheng, Yifan Jing, Wenling Zhou and Guanghui Wang.

2:00 pm in 347 Altgeld Hall,Tuesday, November 19, 2019

Absolute continuity and singularity for probability measures induced by a drift transform of the independent sum of Brownian motion and symmetric stable process

Ruili Song (Nanjing University of Finance and Economics, and UIUC Math)

Abstract: We consider a Levy process $X$ which is the independent sum of a Brownian motion and a symmetric $\alpha$-stable process in $R^d$. The probability measure $P^b$ is induced by the drift transform of $X$ via the vector valued function $b$. We study mutual absolute continuity and singularity of $P$ and $P^b$ on the path space. We also investigate the problem of finiteness of the relative entropy of these measures on $R^d$ ($d\ge 3$).