UIUC Dept. of Mathematics Seminar Calendar

      March 2011             April 2011              May 2011      
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Thursday, April 21, 2011

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Thursday, April 21, 2011

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Submitted by pppollac.

Maria Sabitova (CUNY Math)
Twisted root numbers of elliptic curves over local fields with residual characteristic 3
Abstract: Root numbers are signs in functional equations for L-functions. In this talk I will discuss local twisted root numbers attached to elliptic curves, i.e., signs in functional equations for L-functions attached to an elliptic curve over a local field twisted by a Galois representation. In the computation of local root numbers attached to elliptic curves the most difficult case is when elliptic curves have wild ramification, i.e., when the residual characteristic p of the base field is 2 or 3. The purpose of this talk is to report on results in the case when p=3.

Group Theory Seminar
1:00 pm in Altgeld Hall 347, Thursday, April 21, 2011

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Submitted by kapovich.

Desmond Cummins (UIUC Math)
A geometric introduction to S-machines
Abstract: The S-machine is a model of computation that was first introduced by Mark Sapir. Although an S-machine can be formally defined as a rewriting system consisting of a finite set of rules that act on the set of words is some finite alphabet, a more natural definition can be given in which the S-machine is defined to be a certain type of finitely presented HNN extension of a free group. Using this defintion, computations of the S-machine can be interpreted as VanKampen diagrams over the corresponding finite group presentation. In this talk I will formally define S-machines as finite group presentations and then prove some basic structural results about the VanKampen diagrams that correspond to computations of S-machines.

Analysis Seminar
2:00 pm in 243 Altgeld Hall, Thursday, April 21, 2011

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Submitted by aimo.

Pekka Salmi (University of Waterloo)
Idempotent states on locally compact quantum groups
Abstract: An idempotent state on a locally compact group is just a probability measure that is an idempotent with respect to the convolution. The Kawada-Ito theorem characterizes such idempotent states as the normalised Haar measures of compact subgroups. On the dual side, idempotent states on group C*-algebras are characteristic functions of open subgroups. In this talk we consider idempotent states on co-amenable locally compact quantum groups and discuss the connections between idempotent states, quantum subgroups and invariant C*-subalgebras. This is joint work with Adam Skalski.

Mathematics Colloquium
4:00 pm in 245 Altgeld Hall, Thursday, April 21, 2011

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Submitted by clein.

Vadim Kaimanovich (University of Ottawa)
Random graphs, stochastic homogenization and equivalence relations
Abstract: The idea that one can talk about invariance (or quasi-invariance) of measures not only in the presence of a group of transformations, but also with respect to more sophisticated structures first appeared in geometry in the form of holonomy (quasi-)invariant measures on foliations in mid-70's. Shortly afterwards Feldman and Moore (prompted by ergodic theory motivations) developed a comprehensive theory of measured discrete equivalence relations. As particular cases it included orbit equivalence relations of group actions or induced equivalence relations on transversals of foliations and laminations. Although additional graph structures on equivalence classes had been implicitly used already in the 70's, a formal definition was given only in 1990 by Adams. Graphed equivalence relations have since found numerous applications in ergodic theory. From probabilitic point of view a graphed equivalence relation gives rise to a probability measure on the space of pointed graphs. Moreover, one can just consider probability measures on the latter space invariant with respect to its natural equivalence relation. This idea was first introduced by the author under the name of "stochastic homogenization". Later it was rediscovered by probabilists as "involution invariant" or "unimodular" random networks. In the talk we shall survey this area and discuss its main results and challenges.