Seminar Calendar
for events the day of Thursday, November 12, 2009.

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Thursday, November 12, 2009

Joint Group Theory - Logic Seminar talk
1:00 pm   in Altgeld Hall 347,  Thursday, November 12, 2009
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Submitted by kapovitc.
Paul Schupp (Department of Mathematics, University of Illinois)
Some Questions at the Frontiers of Computer Science
Abstract: In this talk I want to survey some quite different questions which involve all three of the areas mention in the title. First of all, I will discuss the recent remarkable characterization of amenability for finitely generated groups in terms of the classic properties of cellular automata defined over the Cayley graph of the group. Then I will discuss the "remarkable rigidity of randomness" in group theory: In particular, the strong Mostow-type isomorphism rigidity of random groups and the "unreasonably low generic-case complexity" of group-theoretic decision problems. If time permits I will discuss the formal language-theoretic characterizations of virtually free and basic groups and the monadic and temporal logic of such groups.

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Thursday, November 12, 2009
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Submitted by jarouse.
Mat Rogers (UIUC Math)
Three open problems associated with the odd values of the Riemann zeta function
Abstract: While Euler proved that the even values of the Riemann zeta function can be related to powers of pi, there are apparently no such formulas for the odd values of the function. In my talk, I will describe three open problems which naturally arise from this famous question.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, November 12, 2009
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Submitted by rosnbltt.
Chris Wedrychowicz (Indiana University, South Bend)
Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment
Abstract: We extend a result of Calderon and Bellow concerning the a.e convergence of convolution powers of measures having finite second moment. This will be accomplished through weakening the requirement that the Fourier transform of the measure is twice continuously differentiable.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, November 12, 2009
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Submitted by beder.
Alexandra Seceleanu (Department of Mathematics, University of Illinois)
The Syzygy Theorem in Mixed Characteristic
Abstract: The Evans-Griffith Syzygy Theorem states that the rank of a non-free kth syzygy of a module over a equicharacteristic Noetherian local ring is at least k. In the original proof, the height of order ideals of minimal generators for syzygy modules plays a prominent role. I will recall the connection between ranks of syzygies and order ideals and I will introduce a comparison theorem for heights of order ideals of consecutive syzygies modulo a hyperplane section. I will show how one can use this comparison theorem and the Syzygy Theorem in equal characteristic p to prove some relevant cases of the Syzygy Theorem in mixed characteristic.