Department of

Mathematics


Seminar Calendar
for events the day of Monday, September 28, 2015.

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Monday, September 28, 2015

11:00 am in 443 Altgeld Hall,Monday, September 28, 2015

A higher category theorist's take on the spin--statistics theorem

Theo Johnson-Freyd (Northwestern)

Abstract: This talk is about a pair of coincidences in homotopy theory which related quantum field theory with commutative algebra. The first coincidence is the fact that the etale homotopy type of Spec(R) matches the homotopy 1-type of BO(\infty), the classifying space of the stable orthogonal group. This coincidence, I will argue, is the reason for "unitary" phenomena in physics. The second coincidence is a categorification of this: I will describe a setting in which Spec(R) has an "etale" homotopy type that matches the homotopy 2-type of BO(\infty), and explain how this provides the "spin--statistics theorem" relating spinors to fermions.

4:00 pm in 145 Altgeld Hall,Monday, September 28, 2015

Gröbner geometry of Schubert polynomials

Anna Weigandt (UIUC Math)

Abstract: Schubert polynomials were introduced by Lascoux and Schutzenberger in 1982 as a generalization of Schur polynomials. The cohomology of the complete flag variety $Fl_n$ is generated by Schubert classes. We may identify $H^*(Fl_n)\cong Z[x_1,x_2,...x_n]/I^S$ where $I^S$ is the ideal of non-constant symmetric polynomials. Schubert polynomials provide a choice of representatives for the Schubert classes. We will discuss the ideas behind Knutson and Miller's "Gröbner geometry of Schubert polynomials," which gives a geometrically natural explanation for Schubert polynomials.

4:00 pm in 245 Altgeld Hall,Monday, September 28, 2015

C*-algebras - Noncommutative Topological Spaces

Zhong-Jin Ruan (Department of Mathematics, University of Illinois)

4:00 pm in 141 Altgeld Hall,Monday, September 28, 2015

Forcing and Baire category: an introduction

Anton Bernshteyn (UIUC Math)

Abstract: Forcing is a powerful tool invented by Paul Cohen for proving consistency and independence results. As we will see, forcing can be construed as a clever way to use Baire category. In this talk we will outline the method and its application to the independence of the Continuum Hypothesis from ZFC.

5:00 pm in 241 Altgeld Hall,Monday, September 28, 2015

Ternary rings of operators and their linking C*-algebras

Wafaa Albar (UIUC Math)

5:45 pm in Altgeld Hall,Monday, September 28, 2015

Lp estimates on quantum channels

Gao Li (UIUC Math)

Abstract: Quantum channels are completely positive trace preserving (CPTP) maps. I will talk about some Lp norm estimates on "nice" classes of CPTP maps. This is a joint work with Marius Junge and Nicholas LaRacuente. The main tools we use are Haagerup tensor product, GNS construction and complex interpolation. If time permits, I will present some connections to quantum information theory.