Department of

Mathematics


Seminar Calendar
for events the day of Monday, November 27, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 27, 2017

3:00 pm in 141 Altgeld Hall,Monday, November 27, 2017

Nilpotence in Motivic Homotopy Theory

Tsutomu Okano   [email] (UIUC)

Abstract: This talk will be in two (currently unrelated) parts. First I will construct the stable motivic homotopy category by defining the category of GL spectra which is an analogue of the category of orthogonal spectra from topology. I will mention some nice properties of this category and give examples of motivic GL spectra. In the second part of the talk I will introduce the question of nilpotence in motivic homotopy theory. This seems to be a difficult problem since Nishida nilpotence and the Devinatz-Hopkins-Smith theorems do not carry over immediately. I will talk about some approaches that are being used to shed light on these questions.

4:00 pm in 245 Altgeld Hall,Monday, November 27, 2017

Problem-solving, question-asking and knowledge-finding

Bruce Reznick   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Three of the most important activities that researchers perform are listed in the title. I will talk about practical techniques for improving your skills in these areas, using specific examples of mathematics from my own work and the work of my graduate students. My intention that most members of the audience will see at least a few objects which resonate with their own mathematical interests.

5:00 pm in Altgeld Hall 445,Monday, November 27, 2017

Gradient Flows for Quantum Markov Semigroups

Li Gao   [email] (UIUC Math)

Abstract: A large number of classical evolution equations could be viewed as gradient flow in the 2-Wasserstein metric for certain functionals, and that when the functionals were uniformly convex along geodesics of this geometry, a host of functional inequalities such as logarithmic Sobolev inequality were consequently valid. In this talk, I will discuss the recent work of E. A. Carlen and J. Maas on extending this story to quantum Markov semigroups. They show that if an ergodic quantum Markov semigroup satisfies detailed balance condition, then in a noncommutative analog of 2-Wasserstein metric it is the gradient flow for the relative entropy with respect to the equilibrium state. If time permits, I will also mention the connection to functional inequalities.