Modul:   MAT760  Ergodic theory and dynamical systems seminar

Counting Pairs of Saddle Connections

Vortrag von Prof. Dr. Jayadev Athreya

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 25.09.23  Zeit: 15.00 - 16.00  Raum: Y27H25

Motivated by the comparison of sets of holonomies of saddle connections on translation surfaces to Poisson point processes, we show that for almost every translation surface the number of pairs of saddle connections with bounded virtual area has asymptotic quadratic growth. The proof techniques combine ergodic methods for counting saddle connections with the fact that the Siegel--Veech transform is in L2. The talk will not assume prior knowledge of translation surfaces, and we will attempt to keep it broadly accessible. This is joint work with Sam Fairchild and Howard Masur.