UIUC Dept. of Mathematics Seminar Calendar

    September 2010          October 2010          November 2010    
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                        31

Thursday, October 28, 2010

Group Theory Seminar
1:00 pm in 347 Altgeld Hall, Thursday, October 28, 2010

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Submitted by clein.

Enric Ventura (Universitat Politecnica de Catalunya and CRM-Montreal)
The conjugacy problem for some extensions of F_n, Z^m, B_n, and F
Abstract: We will review the main idea in the solution of the conjugacy problem (CP) for free-by-cyclic groups given by Bogopolski-Martino-Maslavova-Ventura in 2006. A close analysis of this argument having the classical Miller's groups in mind (which are free-by-free and have unsolvable conjugacy problem) gave rise to a subsequent and stronger result by the same authors, giving an explicit characterization of the solvability of the conjugacy problem within the family of free-by-free groups. It turns out that the freeness of the base group is irrelevant in the whole proof, and the only crucial property is the solvability of the so-called twisted conjugacy problem (TCP). This way, we shall give characterizations of the solvability of the conjugacy problem for certain families of extensions of groups with solvable TCP. We will discuss the particular cases of extensions of free groups $F_n$, free abelian groups $Z^m$, Braid groups $B_n$, and Thomson's group $F$.

Number Theory
1:00 pm in 241 Altgeld Hall, Thursday, October 28, 2010

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Submitted by berndt.

Kevin Ford (Illinois)
R. I. P.
Abstract: Recently, Candes and Tao showed that a k-sparse vector x in R^N (think of x as a signal) can be effectively recovered from a set of n-dimensional linear measurements with n much smaller than N, if the matrix of the vectors v_i satisfies the Restricted Isometry Property (RIP for short) of order k. All known explicit constructions of RIP matrices make use of number theory, and all have order k=O(sqrt(n)) (we will review these). We give a new explicit construction of RIP matrices of order n^{1/2+c} for some positive c, based on additive combinatorics. This is joint work with J. Bourgain, S. J. Dilworth, S. Konyagin and D. Kutzarova.