Thursday, October 26, 2023
Time  Items 

All day 

4:00pm 
10/26/2023  4:00pm Horospherical group actions on homogeneous spaces are famously known to be extremely rigid. In finite volume homogeneous spaces, it is a special case of Ratnerâ€™s theorems that all horospherical orbit closures are homogeneous. Rigidity further extends in rankone to infinite volume but geometrically finite spaces. The geometrically infinite setting is far less understood. We study Zcovers of compact hyperbolic surfaces and provide the first description of all possible horocycle orbit closures in this category. Surprisingly, the topology and Hausdorff dimension of these nonhomogeneous orbit closures delicately and discontinuously depends on the choice of a hyperbolic metric on the covered compact surface. Nevertheless, some rigidity is preserved in the form of integer Hausdorff dimension of all orbit closures. Based on an ongoing series of works together with James Farre and Yair Minsky. Location:
KT205
10/26/2023  4:00pm This is the sixth talk in the seminar. Location:
KT 801
10/26/2023  4:00pm In their original paper, Kolmogorov, Petrovsky, and Piskunov demonstrated stability of the minimal speed traveling wave with an ingenious compactness argument based on, roughly, the decreasing "steepness" of the profile. This proof is extremely flexible, yet entirely not quantitative. On the other hand, more modern PDE proofs of this fact for general reactiondiffusion equations are highly tailored to the particular equation, fairly complicated, and often not sharp in the rate of convergence. In this talk, which will be elementary and selfcontained, I will introduce a natural if "hidden" quantity, the shape defect function, that allows a simple approach to quantifying convergence to the traveling wave for a large class of reactiondiffusion equations. This is a joint work with Jing An and Lenya Ryzhik. Location:
KT 219
