Event Detail

Event Type: 
Number Theory Seminar
Friday, February 14, 2020 - 15:00 to 15:50
Strand Agricultural Hall (Stag) 213

Speaker Info

University of Pennsylvania

Special guest in class, as seminar talk: In this talk I'll begin by discussing covers of Riemann surfaces, with some concrete examples which are covers of the projective line branched at three points. A famous theorem of Belyi says that any smooth projective curve defined over a number field can be realized as such a cover. This led to Belyi's proof that there is a natural embedding of the absolute Galois group Gal(\overline{Q}/Q)of the rational numbers Q into the group of automorphisms Aut(\hat{F}_2) of a pro-free group on two generators. In this talk I will discuss these ideas and then some work with F. Bleher and A. Lubotzky. This work implies that various natural representations of finite index subgroups of Gal(\overline{Q}/Q) can be lifted to representations of finite index subgroups of Aut(\hat{F}_2). The representations come from the l-adic Tate modules of the generalized Jacobians of curves.