Title - On the non-triviality of arithmetic invariants modulo p

Speaker: Prof. Ashay  Burungale    Time: 3:00pm-5:00pm Mon-Wen   Place: MCM 610

   Abstract - In these talks, we discuss non-triviality of certain arithmetic invariants modulo p. This includes the case of Katz p-adic L-function, its variants, p-adic Abel-Jacobi image and p-adic height of generalised Heegner cycles in Iwasawa theoretic families. In particular, we discuss a new proof and refinement of Mazur's conjecture on the non-triviality of Heegner points. The strategy is inspired by Hida's pioneering work in the case of Katz p-adic L-function relying on Chai's theory of Hecke stable subvarieties of a mod p Shimura variety.