Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, November 10, 2020.

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Tuesday, November 10, 2020

11:00 am in via Zoom,Tuesday, November 10, 2020

R-motivic homotopy theory and the Mahowald invariant

Eva Belmont (Northwestern)

Abstract: Abstract: The Mahowald invariant is a highly nontrivial map (with indeterminacy) from the homotopy groups of spheres to itself, with deep connections to chromatic homotopy theory. In this talk I will discuss a variant of the Mahowald invariant that can be computed using knowledge of the R-motivic stable homotopy groups of spheres, and discuss its comparison to the classical Mahowald invariant. This is joint work with Dan Isaksen.

Please email Jeremiah Heller for Zoom info (jbheller@illinois.edu)

2:00 pm in Zoom,Tuesday, November 10, 2020

Stability from symmetrisation arguments

Oleg Pikhurko (University of Warwick)

Abstract: We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of a limit version of the problem. We present some of its application to the inducibility problem where one maximises the number of induced copies of a given complete partite graph $F$ in an $n$-vertex graph.

This is joint work with Hong Liu, Maryam Sharifzadeh and Katherine Staden.

Please contact Sean at SEnglish (at) illinois (dot) edu for Zoom information.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, November 10, 2020

Entropy dissipation for degenerate diffusion process

Qi Feng (USC)

Abstract: A drift-diffusion process with non-degenerate diffusion coefficient matrix posses good properties (under certain conditions): convergence to equilibrium, entropy dissipation rate, etc. The degenerate drift-diffusion process possess degenerate/rectangular diffusion coefficient matrix, which makes it difficult to govern the convergence property and entropy dissipation rate by drift-diffusion coefficients on its own because of lacking control for the system. In general, the degenerate drift-diffusion is intrinsically equipped with sub-Riemannian struc- ture defined by the diffusion coefficients. We propose a new methodology to systematically study general drift-diffusion process through sub-Riemannian geometry and Wasserstein geometry. We generalize the Bakry-Emery calculus and Gamma z (Baudoin-Garofalo) calculus to define a new notion of sub-Riemannian Ricci curvature tensor. With the new Ricci curvature tensor, we are able to establish generalized curvature dimension bounds on sub-Riemannnian manifolds which goes beyond step two condition. As application, for the first time, we establish analytical bounds for logarithmic Sobolev inequalities for the weighted measure in a compact region on displacement group(SE(2)). Our result also provides entropy dissipation rate for Langevin dynamics with gradient drift and variable temperature matrix. The talk is based on joint works with Wuchen Li.