| On expliquera en détails une conjecture du type théorie de Kisin reliant certains phi modules et des modifications de fibrés sur la courbe. Cette conjecture contient comme cas particulier une classification des groupes p-divisibles sur l'anneau des entiers d'une extension valuée complète algébriquement close des nombres p-adiques. |
| I will report on the current status of my ongoing project with Günter Harder. The aim of this project is to study rank one Eisenstein cohomology for GL(N) to prove rationality results about ratios of critical values for Rankin-Selberg L-functions for GL(n) x GL(n'), where n+n'=N. |
| This is a joint work with Ashay Burungale. I describe a proof of rigidity; i.e., vanishing of a classical mod p Hilbert modular form over one "gothic p"-Serre-Tate coordinate (around an ordinary CM Hilbert modular abelian variety) implies the vanishing of the modular form over the entire Hilbert modular variety. This gives some application to determination of the mu-invariant of the "gothic p"-part of Katz p-adic L-function and its derivative. Here "gothic p" is a factor of a prime p > 3 in the base totally real field. |
| Modularity lifting theorems were introduced by Taylor and Wiles and formed a key part of the proof of Fermat's Last Theorem. Their method has been generalized successfully by a number authors but always with the restriction that the Galois representations in question have regular weight. Moreover, the sought after automorphic representation must come from a group that admits Shimura varieties. I will describe a method to overcome these restrictions, conditional on certain conjectures which themselves can be established in a number of cases. This is joint with Frank Calegari. |
| This documentary is directed by Nandan Kudhyadi and produced by IISER Pune, and Vigyan Prasar, New Delhi, India. It features Ken Ono, A.Raghuram, Srinivasa Rao, and T.V.Venkateswaran walking in the footsteps of Ramanujan trying to fathom his genius. The documentary was shot in Chennai, Erode, Kumbakonam, Nammakal, India, and Cambridge, England. |