Seminar Calendar
for events the week of Saturday, December 10, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, December 6, 2016

Harmonic analysis and differential equations (HADES)
1:00 pm   in 347 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by xcli.
Joris Roos (University of Bonn)
Maximal operators related to curves in the plane
Abstract: The talk will consist of two parts. In the first part, the discussion will focus on an analogue of Carleson's operator associated with integration along a monomial curve. In that context it is natural to ask whether the methods of time-frequency analysis carry over to an anisotropic setting. We answer that question and also provide certain partial bounds for the Carleson operator along monomial curves using entirely different methods. In the second part, I will present some results for maximal operators and Hilbert transforms along variable curves. Apart from the intrinsic interest in these operators, another motivation stems from Zygmund's conjecture on differentiation along Lipschitz vector fields. In particular, we can prove a curved variant of the conjecture.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by anush.
Chieu Minh Tran (UIUC Math)
Tame structure via bounds on multiplicative character sums over finite fields
Abstract: We study the model theory of the structure $(F; <)$ where $F$ is the algebraic closure of the field of $p$ elements and $<$ is an ordering on $F^\times$ induced by an injective group homomorphism $\chi: F^\times \to \mathbb{C}^\times$. Various notions of model theoretic tameness of the structure turn out to be consequences of number theoretic behaviors of the character map $\chi$. The results obtained are the first steps in bringing number theoretic phenomena of this type into model theory, following a suggestion by van den Dries, Hrushovski and Kowalski.

Graduate Student Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by compaan2.
Terry Harris   [email] (UIUC Math)
Different types of convexity for two-by-two matrices
Abstract: I will introduce some generalized notions of convexity and explain how they arise from the calculus of variations. Then I will talk specifically about rank-one convexity for two-by-two matrices.

Graduate Student Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by jli135.
Scott Ahlgren   [email] (UIUC)
The eta function
Abstract: The Dedekind eta function is one of the fundamental functions of number theory. It is a basic building block for many types of modular forms, and it plays a central role in a range of number-theoretic problems. I will give a bunch of examples of objects which can be built using the eta function, and of the applications which are related to its properties.

Graduate Student Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by jli135.
Scott Ahlgren   [email] (UIUC)
The eta function
Abstract: The Dedekind eta function is one of the fundamental functions of number theory. It is a basic building block for many types of modular forms, and it plays a central role in a range of number-theoretic problems. I will give a bunch of examples of objects which can be built using the eta function, and of the applications which are related to its properties.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by rtramel.
John Calabrese (Rice University)
To Be Announced

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, December 6, 2016
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Submitted by molla.
Spencer Gordon (Illinois Computer Science)
The complexity of the Colorful Carathéodory Theorem and other total search problems
Abstract: The Colorful Carathéodory Theorem states that given sets $P_1,\dotsc,P_{d+1} \subseteq \mathbb{R}^d$ such that the origin is in the convex hull of each of the $P_i$, there exists a $(d+1)$-point "colorful" set $S \subseteq P_1 \cup P_2 \cup \dotsb \cup P_{d+1}$ with $|S \cap P_i| = 1$ for each $i$ such that the origin is in the convex hull of $S$. The proof of this theorem gives an algorithm for finding such a colorful set, but it can take time exponential in $d$. We discuss the complexity of finding a colorful set containing the origin and situate this problem in complexity hierarchy of total search problems.

Wednesday, December 7, 2016

Integrability and Representation Theory
3:00 pm   in 241 Altgeld Hall,  Wednesday, December 7, 2016
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Submitted by nevins.
Ana Balibanu (University of Chicago)
The Peterson variety and the wonderful compactification
Abstract: We look at the centralizer in a complex semisimple algebraic group $G$ of a regular nilpotent $e\in \operatorname{Lie}(G)$ and show that its closure in the wonderful compactifi cation $\overline{G}$ is isomorphic to the Peterson variety. We generalize this result to show that for any regular $x\in \operatorname{Lie}(G)$, the closure of the centralizer $G^x$ in $\overline{G}$ is isomorphic to the closure of a general $G^x$-orbit in the flag variety. We consider the family of all such centralizer closures and show that it has a natural Poisson structure.

Thursday, December 8, 2016

Math-Physics Seminar
12:30 pm   in 345 Altgeld Hall (NOTE: change of location),  Thursday, December 8, 2016
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Submitted by katz.
Dave Morrison (UC Santa Barbara, Departments of Mathematics and Physics)
Little string theories via F-theory
Abstract: Little string theories are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. I will present a systematic approach to the construction of supersymmetric little string theories via F-theory. This is joint work with Lakshya Bhardwaj, Michele Del Zotto, Jonathan Heckman, Tom Rudelius, and Cumrun Vafa.


1:00 pm   in 239 Altgeld Hall,  Thursday, December 8, 2016
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Submitted by tyson.
IGL Fall 2016 Open House
Abstract: End of semester poster presentations by IGL project teams. Come see what research has been done in the IGL this semester!

Analysis Seminar
11:00 pm   in 243 Altgeld Hall,  Thursday, December 8, 2016
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Submitted by tumanov.
Rami Luisto (UCLA)
Stoilow's theorem revisited
Abstract: Stoilow's theorem states that any continuous, open and light map from a planar domain to the plane is locally a holomorphic map up to a conjugation with homeomorphisms. From this local fact it follows that up to a homeomorphic change of coordinates a continuous, open and light map between two orientable topological surfaces is a holomorphic map between Riemann surfaces. In this talk we give a modern proof for the local result and, time permitting, discuss how the local result gives rise to the global version.