Department of

Mathematics


Seminar Calendar
for events the day of Thursday, January 30, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, January 30, 2014

1:00 pm in 347 Altgeld Hall,Thursday, January 30, 2014

Recent results on generalized Baumslag-Solitar groups

Derek Robinson (UIUC Math)

Abstract: A generalized Baumslag-Solitar group is the fundamental group of a graph of groups with infinite cyclic edge and vertex groups. Such groups are of algebraic, combinatorial and topological interest. A survey will be given of recent work on GBS-groups, including computation of the center and maximal cyclic normal subgroup of GBS-groups and also the relation with 3-manifold groups.

2:00 pm in 243 Altgeld Hall,Thursday, January 30, 2014

Lipschitz equivalence of fractal sets

Huojun Ruan (Zhejiang University)

Abstract: We will mainly talk about recent results on Lipschitz equivalence of fractal sets, including: 1) Dust-like self-similar sets, especially those with two branches. 2) Self-similar sets with touching structure in the one dimensional case, related with the so-called {1,3,5}-{1,4,5} problem posed by David and Semmes in 1997. 3) Lipschitz equivalence of Sierpinski carpets.

2:00 pm in 140 Henry Administration Building,Thursday, January 30, 2014

On certain properties of the Cohen-Ramanujan sum

Nicolas Robles (University of Zurich)

Abstract: The Cohen-Ramanujan sum is a generalization of the Ramanujan sum defined by \begin{align} \label{cohendef} c_q^{(\beta )}(n) = \sum\limits_{{{(h,{q^\beta })}_\beta } = 1} {{e^{2\pi inh/{q^\beta }}}}, \nonumber \end{align} where $h$ ranges over the the non-negative integers less than $q^{\beta}$ such that $h$ and $q^{\beta}$ have no common $\beta$-th power divisors other than $1$. In this talk we will study several arithmetical and analytical properties of these sums. In particular we will derive their explicit formulae, their connection to the Riemann Hypothesis, and their moments which are defined by \[{C_k^{(\beta)}}(x,y) = \sum\limits_{n \leqslant y} {{{\bigg( {\sum\limits_{q \leqslant x} {{c_q^{(\beta)}}(n)} } \bigg)}^k}}, \] where $k$ is a positive integer and $x$ and $y$ are large reals. Joint work with Patrick K\"{u}hn.

4:00 pm in 245 Altgeld Hall,Thursday, January 30, 2014

Mean field Spin Glasses: Extreme values and Energy Landscape

Antonio C. Auffinger (University of Chicago)

Abstract: Spin glasses are magnetic systems exhibiting both quenched disorder and frustration, and have often been cited as examples of "complex systems." As mathematical objects, they provide several fascinating structures and conjectures. This talk will cover the history of these models focusing on properties of the energy landscape and their extreme values.