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.