## Cohomological interpretation of L-values

## On the exceptional zeros of p-adic L-functions of Hilbert modular forms

The use of modular symbols to attach p-adic Lfunctions to Hecke eigenforms goes back to the work of Manin et al in the 70s.

## The Beilinson-Flach Euler system

In this talk, I will set up the general Euler system machinery of Rubin and look at its properties and examples.

## A bounded Beilinson-Flach Euler system for a pair of non-ordinary forms

Building on the previous talk, I will set up the construction of a (flat, sharp) integral Euler system associated to the Rankin-Selberg product for a pair of non-ordinary modular forms and also show the Iwasawa theoretic results one can obtain from the same.

## Applications of Goncharov’s conjectures to point-counting

The classical theory of multiple polylogarithms found a wealth of interesting relations between interesting transcendental numbers.

## Universal Deformations of dihedral representations

Given a 2-dimensional dihedral representation of a profinite group over a finite field, we will give necessary and sufficient conditions for its universal deformation to be dihedral.

## Indefinite theta series via incomplete theta integrals

In this talk we will give an introduction to recent developments -in particular motivated by mathematical physics- in the theory of indefinite theta series. This is joint with Steve Kudla (Toronto).

## p-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou

I will report joint work in progress with R.Pollack and S.Sasaki, where we prove a p-adic Gross-Zagier formula for critical slope p-adic L-functions.

## On the Bloch-Kato conjecture for automorphic polarized motives

The goal of these lectures is to present a proof towards some results predicted by the Bloch-Kato conjecture giving a link between the order of vanishing of the L-function of a motive and the rank of the corresponding Bloch-Kato-Selmer group.

## On the Bloch-Kato conjecture for automorphic polarized motives

The goal of these lectures is to present a proof towards some results predicted by the Bloch-Kato conjecture giving a link between the order of vanishing of the L-function of a motive and the rank of the corresponding Bloch-Kato-Selmer group.