Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 29, 2016.

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Thursday, September 29, 2016

11:00 am in 241 Altgeld Hall,Thursday, September 29, 2016

Ramanujan's formula for $\zeta(2n+1)$

Bruce Berndt (Illinois Math)

Abstract: Let $\zeta(s)$ denote the Riemann zeta function. If $n$ is a positive integer, a famous formula of Euler provides an elegant evaluation of $\zeta(2n)$. However, little is known about $\zeta(2n+1)$. In Ramanujan's earlier notebooks, we find a formula for $\zeta(2n+1)$ which is a natural analogue of Euler's formula. We provide its history, indicate why it is "interesting," and show its connections with other mathematical objects such as the Dedekind eta function, Eisenstein series, and period polynomials.

12:30 pm in 464 Loomis Laboratory,Thursday, September 29, 2016

Deformation classes of unitary invertible field theories

Dan Freed (University of Texas Math)

Abstract: The phase, or deformation class, of a quantum mechanical system determines its large-scale features. If we can approximate the long-range properties by a field theory, then we can bring to bear the Axiom System for field theory initiated by Segal. In joint work with Mike Hopkins we carry this out for invertible field theories using techniques from (equivariant) stable homotopy theory. The results apply immediately to the classification of short range entangled lattice systems in condensed matter physics. The new conceptual ingredient is an extended notion of unitarity for invertible topological theories. The explicit computations are via the Adams spectral sequence.

2:00 pm in 243 Altgeld Hall,Thursday, September 29, 2016

Characterization and construction of conical 3-uniform measures

A. Dali Nimer (University of Washington)

4:00 pm in Altgeld Hall 245,Thursday, September 29, 2016

Lecture 3. Subfactors, conformal field theory and the Thompson group

Vaughan Jones (Vanderbilt University)

Abstract: Subfactors actually arise in conformal field theory as shown by Wassermann for theories where space-time is actually the circle. It is tempting to speculate that all subfactors arise in this way but the famous Haagerup factor has not yet been obtained. The Thompson groups are certain countable groups of homeomorphisms of the circle which can be thought of as approximations to the group of diffeomorphisms of the circle which is an essential ingredient of conformal field theory. In an attempt to get at CFT’s from subfactors like the Haagerup we obtain interesting unitary representations of the Thompson groups which allow us to show that this approach can never work! As a consolation prize we present a construction of all knots and links showing that a Thompson group is as good as the braid groups at constructing knots and links.