Number Theory Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Altgeld Hall 347
- Date
- Feb 4, 2025 11:00 - 11:50 am
- Speaker
- Aaron Landesman (Harvard)
- Contact
- Jesse Thorner and Yuan Liu
- jat9@illinois.edu and yyyliu@illinois.edu
- Views
- 70
- Originating Calendar
- Number Theory Seminar Calendar
Title: The Cohen-Lenstra moments over function fields
Abstract:
The Cohen-Lenstra heuristics are influential conjectures in arithmetic statistics from 1984 which predict the average number of p-torsion elements in class groups of quadratic fields, for p an odd prime. So far, this average number has only been computed for p = 3. In joint work with Ishan Levy, we verify this prediction for arbitrary p over suitable function fields. The key input to the proof is a computation of the stable homology of Hurwitz spaces associated to dihedral groups. The algebraic geometry seminar later today will be, in some sense, a continuation of this talk.