Seminar Calendar
for events the day of Thursday, April 28, 2011.

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Thursday, April 28, 2011

Number Theory
1:00 pm   in 241 Altgeld Hall,  Thursday, April 28, 2011
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Submitted by berndt.
George Andrews (Pennsylvania State University)
Partitions with Early Repetitions and Slater's List
Abstract: In 1886, J.J. Sylvester defined "flushed partitions", and posed a couple of interesting problems concerning them. Subsequently in 1970, I wrote a short paper on Sylvester's questions and in 2009 considered, more generally, partitions with early repetitions. One result in the latter paper involves one of the seventh order mock theta functions. Sylvester's ideas and the subsequent refinements lead one to ask if there are similar interpretations for some or many of the identities in Slater's compendium of Rogers-Ramanujan type identities and if this leads to new discoveries. The object of this talk is to provide an affirmative answer with numerous results of this nature.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 28, 2011
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Submitted by kapovich.
Igor Mineyev (UIUC Math)
Submultiplicativity: how to prove the Hanna Neumann Conjecture
Abstract: The Hanna Neumann Conjecture (HNC) asserts an explicit upper bound on the rank of the intersection of two finitely generated subgroups of a free group. I will use the Murray-von Neumann dimension of Hilbert modules to state a general submultiplicativity property for complexes with actions by a group. Then I will outline a proof of submultiplicativity in the case of graphs and free groups. This implies the Strengthened Hanna Neumann Conjecture.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 28, 2011
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Submitted by aimo.
Dustin Mayeda (University of California at Davis)
On Cusp Finiteness for higher dimensional Kleinian groups with critical exponent less than one
Abstract: In the late 1970's Sullivan proved that a finitely generated three dimensional Kleinian group has only finitely many cusps. The straight forward generalization of Sullivan's theorem to higher dimensions does not hold as shown by examples of Kapovich and Potyagailo. I will discuss a condition on higher dimensional Kleinian groups which implies that they have finitely many cusps.

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, April 28, 2011
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Submitted by lukyane2.
Ben Reiniger (UIUC Math)
Coxeter Groups and Aspherical Manifolds
Abstract: We'll start by defining Coxeter groups and noting some nice properties. Then we'll describe a construction of a topological space from a given group and space, note some nice properties, then apply it to the specific case of Coxeter groups. We'll then see how this creates a counterexample to a conjecture regarding aspherical manifolds.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 28, 2011
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Submitted by berndt.
George Andrews (Pennsylvania State University)
Partition Function Differences, Ehrenpreis's Problem and the Anti-Telescoping Method
Abstract: For decades partition function differences have been studied. These include a famous problem of Henry Alder posed in the 1950's and solved only recently by Yee, Oliver et al.. In 1978, Szekeres and Richmond partially solved a problem of this type concerning the Rogers-Ramanujan continued fraction. Unknown to them, the problem had essentially been solved by Ramanujan in the Lost Notebook. In this talk, I will begin with the history of such problems. I will conclude with some observations on a general method for treating some of these problems. Here is a typical example of the questions posed. The late Leon Ehrenpreis asked in 1987 if one could prove that the number of partitions of n into parts congruent to 1 or 4 mod 5 is always at least as large as the number with parts congruent to 2 or 3 mod 5 WITHOUT using the Rogers-Ramanujan identities. Subsequently Baxter and I gave a "sort of" solution to the problem, and Kevin Kadell gave a complete solution in 1999.