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Alessia Elisabetta Kogoj, University of Urbino "Carlo Bo"
Several Liouville-type theorems are presented, related to evolution equations on Lie Groups and to their stationary counterpart. Our results apply in particular to the heat operator on Carnot groups, to linearized Kolmogorov operators and to operators of Fokker-Planck-type like the Mumford operator. An application to the uniqueness for the Cauchy problem is also shown.
These results are based on joint publications with A. Bonfiglioli, E. Lanconelli, Y. Pinchover and S. Polidoro.
Xinyi Li, University of Chicago
In this talk, I will talk about loop-erased random walk (LERW) in three dimensions. I will first give an asymptotic estimate on the probability that 3D LERW passes a given point (commonly referred to as the one-point function). I will then talk about how to apply this estimate to show that 3D LERW as a curve converges to its scaling limit in natural parametrization. If time permits, I will also talk about the asymptotics of non-intersection probabilities of 3D LERW with simple random walk. This is a joint work with Daisuke Shiraishi (Kyoto).
Michael Landry, Yale University
Let \(M\) be a closed hyperbolic 3-manifold which fibers over \(S^1\), and let \(F\) be a fibered face of the unit ball of the Thurston norm on \(H^1(M;R)\). By results of Fried, there is a nice flow on \(M\) naturally associated to \(F\). We study surfaces which are almost transverse to \(F\) and give a new characterization of the set of homology directions of \(F\) using Agol’s veering triangulation of an auxiliary cusped 3-manifold.
Stephane Mollier, INRIA Grenoble Rhone-Alpes
There are no conferences this week.