MS Seminar (Mathematics - String Theory)

Speaker: Yasuhiro Wakabayashi (Kyoto U)
Title: A theory of opers in positive characteristic and Joshi's conjecture
Date: Fri, Jan 16, 2015, 13:30 - 15:00
Place: Seminar Room B
Abstract: A(n) (dormant) oper, being our central object of this talk, is a certain principal homogeneous space on an algebraic curve (in positive characteristic) equipped with an integrable connection. The study of dormant opers and their moduli may be linked to various fields of mathematics,e.g., p-adic Teichmuller theory developed by Shinichi Mochizuki, geometric Langlands program, Gromov-Witten theory, and combinatorics of rational polytopes (and spin networks), etc. In this talk, we would like to give an overview of a theory of opers in positive characteristic and to present some related results, including an explicit formula for the generic number of dormant opers, which was conjectured by Kirti Joshi.