Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 26, 2016.

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Tuesday, January 26, 2016

11:00 am in 345 Altgeld Hall,Tuesday, January 26, 2016

Towards a minimal projective resolution of bu<0>

Kirsten Wickelgren (Georgia Tech)

Abstract: Arone and Lesh have constructed sequences of spectra interpolating between certain spectra and the Eilenberg-MacLane spectrum HZ, and in certain cases relate their sequences to Goodwille and Weiss towers. They furthermore have conjectures relating their filtration of bu, the Weiss tower for V \mapsto BU(V), and a bu-analogue of the Whitehead conjecture. This talk will present aspects of this work of Arone and Lesh, and then discuss joint work with Julie Bergner, Ruth Joachimi, Kathryn Lesh, and Vesna Stojanoska towards proving these conjectures.

12:00 pm in Altgeld Hall 243,Tuesday, January 26, 2016

Slowly converging Pseudo-Anosovs

Mark Bell (UIUC Math)

Abstract: A classic property of pseudo-Anosov mapping classes is that they act on PML with north-south dynamics. This means that for such a mapping class laminations converge exponentially towards its stable lamination under iteration. We will discuss a new result which shows that (whenever the surface is sufficiently complex) there are pseudo-Anosovs where this convergence is exponential but arbitrarily slow, that is, with base arbitrarily close to one. This work is joint with Saul Schleimer.

1:00 pm in 341 Altgeld Hall,Tuesday, January 26, 2016

Symplectic non-squeezing for the discrete nonlinear Schr\"odinger equation

Alexander Tumanov (UIUC Math)

Abstract: The celebrated Gromov's non-squeezing theorem of 1985 says that the unit ball $B^n$ in $C^n$ can be symplectically embedded in the "cylinder" $rB^1 \times C^{n-1}$ of radius r only if $r\ge 1$. I recall this result and its version for Hilbert spaces. I give an application to the discrete nonlinear Schr\"odinger equation. This work is joint with Alexander Sukhov

2:00 pm in 347 Altgeld Hall,Tuesday, January 26, 2016

Estimates of Dirichlet heat kernel for symmetric Markov processes

Panki Kim (Seoul National University)

Abstract: In this talk, We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Le\'vy processes with weak scaling conditions. We first establish sharp two-sided heat kernel estimates for this processes in $C^{1,\rho}$ open sets. As a corollary of our main result, we obtain a sharp two-sided Green function and a scale invariant boundary Harnack inequality with explicit decay rates in $C^{1,\rho}$ open sets. This is a joint work with Tomasz Grzywny and Kyung-Youn Kim.

3:00 pm in 241 Altgeld Hall,Tuesday, January 26, 2016

New Developments in Hypergraph Ramsey Theory

Dhruv Mubayi   [email] (UIC Math)

Abstract: I will present new results on some Ramsey problems for hypergraphs. For example, I will show a superexponential lower bound for the classical 4-uniform hypergraph Ramsey number r_4(5,n), which represents the first significant progress on this problem since it was considered by Erdős and Hajnal in 1972. I will also show an upper bound for the Erdős-Rogers hypergraph function which is substantially smaller than the previous bound for this problem due to Dudek and the speaker and Conlon-Fox-Sudakov. If time permits, several other results may be presented. Most of this is joint work with Andrew Suk.

4:00 pm in 243 Altgeld Hall,Tuesday, January 26, 2016

Microlocal methods for type A rational Cherednik algebras

Josh Wen (UIUC Math)

Abstract: Given a complex semisimple Lie algebra $\mathfrak{g}$ with Cartan subalgebra $\mathfrak{t}$ and Weyl group $W$, the rational Cherednik algebras $H_c$ are certain deformations of the smash product of $\mathcal{D}(\mathfrak{t})$ with $W$. Some structures from the study of the universal enveloping algebra $U(\mathfrak{g})$ have analogues for $H_c$: for example the PBW filtration and category $\mathcal{O}$. For $\mathfrak{g}=\mathfrak{gl}_n$, Kashiwara and Rouquier constructed a sheaf of micro-differential operators on $Hilb_n(\mathbb{C}^2)$ whose global sections are isomorphic to the spherical subalgebra of $H_c$. Thus, in this case, $H_c$ is to the Hilbert scheme as (primitive quotients of) $U(\mathfrak{g})$ is to the flag variety. In this microlocal framework, McGerty then computed the characteristic cycles of standard modules, relating multiplicities in category $\mathcal{O}$ to the combinatorics of Kostka numbers. I'll present these constructions and suggest a way to move beyond type A which would establish some sort of 'microlocal McKay correspondence'.