Maxim Kirsebom - On a Limiting Distribution for Maximal Cusp Excursions of the Unipotent Flow

Explore a 55-minute lecture on the limiting distribution for maximal cusp excursions of the unipotent flow, presented by Maxim Kirsebom at the Hausdorff Center for Mathematics. Delve into the ergodicity of the unipotent flow on the unit tangent bundle of the modular surface and its identification with PSL_2(R)/PSL_2(Z). Examine the nature of orbit excursions into the cusp, building upon Athreya and Margulis' logarithm law for maximal excursions. Investigate a more precise description of this behavior, focusing on the probability of deepest excursions failing to outperform expected asymptotic behavior. Learn about the application of extreme value statistics and geometry of numbers in this context. Follow the lecture's progression through introduction, setting, geometric interpretation, lattices in R2, partial answers, and the process of finding the measure. Gain insights into ongoing research conducted jointly with Keivan Mallahi-Karai, presented as part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference on "Dynamics on homogeneous spaces."

Introduction
Setting
Geometric interpretation
Lattices in R2
Partial answer
Geometry of numbers
Finding the measure