Department of

Mathematics


Seminar Calendar
for events the day of Thursday, March 6, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, March 6, 2014

11:00 am in 241 Altgeld Hall,Thursday, March 6, 2014

Partition functions and mock theta functions modulo 2 and 3

Scott Ahlgren (UIUC Math)

Abstract: 2 and 3 are often the oddest primes. We will attempt to classify congruences mod 2 and 3 for various partition functions, weakly holomorphic modular forms, and mock theta functions. This generalizes Radu’s recent groundbreaking work on Subbarao’s conjecture for the ordinary partition function. Joint work with B. Kim.

1:00 pm in 347 Altgeld Hall,Thursday, March 6, 2014

The Malnormal Special Quotient Theorem

Daniel Groves (Illinois-Chicago)

Abstract: Wise's Malnormal Special Quotient Theorem (MSQT) is one of the key technical tools in his work on groups with a quasiconvex hierarchy, and a key ingredient in Agol's proof of the Virtual Haken Conjecture. I will explain the role of the MSQT in this story, and outline a new proof due to Agol, Manning and myself.

2:00 pm in 243 Altgeld Hall,Thursday, March 6, 2014

Wolfe's theorem for weakly differentiable cochains

Kai Rajala (University of Jyväskylä)

Abstract: The classical Wolfe's theorem isometrically identifies the space of Whitney flat forms with the space of flat cochains (Whitney flat forms are differential forms whose coefficients as well as the coefficients of the exterior derivatives are bounded). We define weakly differentiable cochains using the notion of upper gradient, introduced for functions by Heinonen and Koskela. We then apply these cochains to generalize Wolfe's theorem to the Sobolev space setting. This is joint work with Camille Petit and Stefan Wenger.

2:00 pm in 140 Henry Administration Building,Thursday, March 6, 2014

Simple continued fractions with occasional large partial quotients

Michael Oyengo (UIUC Math)

Abstract: The continued fraction expansion of certain numbers display surprisingly large partial quotients. We follow the approach by van der Poorten and Shallit of specializing to an integer, the variable in a continued fraction of a Laurent series. It is then easy to tell how and when these large partial quotients occur in the continued fraction expansion of such numbers with a Laurent series representation. We then give well known examples of numbers with this interesting phenomenon.

4:00 pm in 245 Altgeld Hall,Thursday, March 6, 2014

String manifolds and loops

Richard Melrose (MIT)

Abstract: I will start by discussing the (Whitehead) sequence of successively obstructed structures which may exists on a manifold -- orientation, Spin, String. The analytic difficulties in 'exploiting' the existence of a String structure are substantial and I will discuss an approach with Chris Kottke, which builds on ideas of Atiyah, Witten, Brylinski, Stolz and Teichner and Waldorf, through the loop space of the manifold.