Taylor McAdam- Almost-Prime Times in Horospherical Flows

Explore an advanced mathematics lecture on almost-prime times in horospherical flows, delivered by Taylor McAdam at the Hausdorff Center for Mathematics. Delve into effective dynamical results for horospherical flows on the space of lattices using the "thickening" method of Margulis. Discover how these findings are applied to study the distribution of almost-prime times in horospherical orbits and their connection to Sarnak's Mobius disjointness conjecture. Examine topics such as the space of lattices, subgroup actions, rigidity of horospherical actions, equidistribution of primes, and the horocycle flow at prime times. Gain insights into qualitative and effective equidistribution of continuous flows and arithmetic progressions in this 42-minute presentation, part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference.

Intro
The Space of Lattices
Subgroup Actions
Horospherical Subgroups
Rigidity of Horospherical Actions
Equidistribution of Primes
Möbius Disjointness
The Horocycle Flow at Prime Times
Almost-Primes in Horospherical Flows
Qualitative Equidistribution of the Continuous Flow
Effective Equidistribution of the Continuous Flow
Effective Equidistribution of Arithmetic Progressions