Seminar Calendar
for events the day of Thursday, October 13, 2011.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 13, 2011

BCDE Math/Physics Seminar
12:00 pm   in 464 Loomis Laboratory,  Thursday, October 13, 2011
 Del Edit Copy
Submitted by katz.
 Sue Tolman (UIUC Math)Equivariant cohomology and the Duistermaat-Heckman function

Harmonic Analysis and Differential Equations
1:00 pm   in 445 Altgeld Hall,  Thursday, October 13, 2011
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Submitted by laugesen.
 Daniel Grieser   [email] (U. Oldenburg)The plasmonic eigenvalue problemAbstract: (Note the UNUSUAL DAY AND ROOM.) Plasmonics is a modern area of physics where one studies the interaction of electromagnetic waves with the free electrons of a metal ("plasma"). One of the fundamental problems is to determine the resonance frequencies at which this interaction is large. Mathematically this leads to a boundary value problem for harmonic functions in which the resonance frequency is a parameter in the boundary conditions. In the talk I will explain the problem and some results about the resonance frequencies.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, October 13, 2011
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Submitted by kapovich.
 Brian Ray (UIUC Math)Spectral Rigidity in Free Groups.Abstract: We say a subset $\Sigma \subseteq F_N$ of the free group of rank $N$ is \emph{spectrally rigid} if whenever $T_1, T_2 \in cv_N$ are $\mathbb{R}$-trees in (unprojectivized) outer space for which $\| \sigma \|_{T_1} = \| \sigma \|_{T_2}$ for every $\sigma \in \Sigma$, then $T_1 = T_2$ in $cv_N$. Recent results by Carette, Francaviglia, Kapovich, and Martino motivate the following question: is it true that for any $H \leq Aut(F_N)$ either for every $1 \neq g \in F_N$, the orbit $Hg$ is rigid or for every $1 \neq g \in F_N$, the orbit $Hg$ is not rigid? We will explain why, in the case $H$ is cyclic, the orbit $Hg$ is never rigid. We will also show that if we impose additional structure on the set $\Sigma$, then we can establish an equivalence between spectral rigidity and a certain weak aperiodicity'' property.

Number Theory
1:00 pm   in 241 Altgeld Hall,  Thursday, October 13, 2011
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Submitted by berndt.
 Trevor Wooley (University of Bristol)Vinogradov's mean value theorem via efficient congruencingAbstract: We discuss an approach to establishing Vinogradov's mean value that comes within a factor 2 of the optimal number of variables. We will briefly note some applications, but aim to give a reasonably comprehensible introduction to the method. If time permits, we will mention some of the most recent developments.

2:00 pm   in 241 Altgeld Hall,  Thursday, October 13, 2011
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Submitted by lukyane2.
 Brian Collier (UIUC Math)What are connections and what are they good for?Abstract: The main goal of this talk is to introduce connections on holomorphic and hermitian vector bundles so that next weeks speaker has a basic tool box. We will define vector bundles and connections then focus on hermitian connections. Hopefully by the end we will arrive at a more geometric/intuitive way of defining/understanding connections.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 13, 2011
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Submitted by aimo.
 Pekka Pankka (University of Helsinki, Finland)Quasisymmetric (non-)parametrization of Semmes spacesAbstract: In Thirty-three yes or no questions about mappings, measures, and metrics'' Heinonen and Semmes asked whether a decomposition space $\mathbb R^3/\mathrm{Bd}$ associated to Bing's double admits an Ahlfors $3$-regular and locally linearly contractible metric so that the product space $\mathbb R^3/\mathrm{Bd} \times \mathbb R^m$ is not quasisymmetrically equivalent to $\mathbb R^{3+m}$. This question has its origin in the program of understanding the quasiconformal geometry and analysis on metric spaces homeomorphic to Euclidean spaces and, in particular, in a result of Semmes showing that such good metrics without good parametrizations exist for $\mathbb R^3/\mathrm{Bd}$. Recently Heinonen and Wu answered positively to a related question of Heinonen and Semmes on the stabilized decomposition spaces $\mathbb R^3/\mathrm{Wh} \times \mathbb R^m$ associated with the Whitehead continuum. In this talk, I will discuss Semmes type geometrization of more general classes of decomposition spaces $\mathbb R^3/G$ and quasisymmetric (non-)parametrizability results for $\mathbb R^3/G\times \mathbb R^m$, that include the topologically self-similar cases of Whitehead continuum and Bing's double. This is a joint work with Jang-Mei Wu.