Department of

Mathematics

Seminar Calendar
for events the day of Monday, October 5, 2015.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 5, 2015

4:00 pm in 145 Altgeld Hall,Monday, October 5, 2015

A geometric construction of moduli spaces of semistable sheaves

Yun Shi (UIUC Math)

Abstract: Classification of vector bundles is an important problem in algebraic geometry. It naturally leads to the study of moduli spaces of bundles. To obtain a nice scheme structure for the moduli spaces, one restricts the objects of interest to semistable bundles. Through the compactification of the moduli spaces, one naturally encounters non-locally free sheaves. In this talk, we will introduce a geometric construction of moduli spaces of semistable sheaves. By showing stability condition for coherent sheaves and stable points in the GIT sense amount to the same constraint, we construct the moduli space of semistable sheaves as a GIT quotient of an open subscheme of the Quot-scheme.

4:00 pm in 245 Altgeld Hall,Monday, October 5, 2015

Integrable Systems and Representation Theory

Maarten Bergvelt (Department of Mathematics, University of Illinois)

Abstract: "Special" functions are functions that at last some mathematicians care about. Experience has shown that many (all?) special functions come from representation theory and are solutions of integrable systems. A gentle introduction and examples are given.

4:00 pm in 141 Altgeld Hall,Monday, October 5, 2015

Forcing and Baire category: continued

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, October 5, 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.