Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## Seminar on Kac-Moody algebras and related topics

## A p-adic family of Saito-Kurokawa lifts for a Coleman family and the Bloch-Kato conjecture

We will construct a $p$-adic family of Saito-Kurokawa lifts for a Coleman family and extend the result of Agarwal and Brown on the Bloch-Kato conjecture for elliptic modular forms of low weights to higher weights. More precisely, we will prove that the $p$-valuation of the order of the Selmer group of a Coleman deformation is bounded below by the $p$-valuation of the algebraic part of the critical $L$-value attached to the initial Hecke eigenform of a Coleman family satisfying some reasonable assumptions given by Agarwal and Brown.

## Motivic obstruction to rationality of a very general cubic hypersurface in P^5

## Eisenstein and CM congruence modules defined over a real quadratic filed

Measuring congruences among modular forms over arithmetic rings has good applications

to number theory. In particular, Hida has shown in 2013 that the non-existence of the following

two types of congruences is almost equivalent to the vanishing of the $\mu$-invariants of the

Kubota-Leopoldt $p$-adic $L$-function and the Katz anti-cyclotomic $p$-adic $L$-function:

(1) a congruence mod $p$ between a $p$-adic family of Eisenstein series and a non-CM

cuspidal Hida family; (2) a congruence mod $p$ between a non-CM and a CM cuspidal

## Niebur-Poincaré Series and Regularized Inner Products

Zagier introduced weight 2k cusp forms f_{k,D} associated to quadratic forms of positive

discriminant D. We determine the Fourier coefficients of analogues of these functions of

weight 2, higher level, and negative discriminant and relate them to traces of singular moduli

of Niebur-Poincaré series. This allows us to compute regularized inner products of these

functions, which in the higher weight case have been related to evaluations of higher

Green's functions at CM-points.

## New guests at the MPIM

## Construction of vector valued Siegel modular forms and examples of congruences

I will talk about construction vector valued Siegel modular forms (of any vector valued weight) by theta series with pluri-harmonic polynomials. And I will show examples congruences concerning Hecke eigenforms of degree three which are conjectural lift conjectured by Bergstroem, Faber and van der Geer. This talk is based on a joint work with Professor Ibukiyama. If time permits, I would like to talk about congruences concerning with other lifts also.

## Siegel modular forms with respect to non-split symplectic groups

We denote by $G$ the unitary group of the quaternion hermitian

space of rank two over an indefinite quaternion algebra $B$ over

the rational number field. Then the group $G$ is a $Q$-form of $\operatorname{Sp}(2;\mathbb{R})$,

and each $Q$-form of $\operatorname{Sp}(2;\mathbb{R})$ can be obtained in this way.

In this talk, we will consider Siegel modular forms for discrete

subgroups of $\operatorname{Sp}(2;\mathbb{R})$ which are defined from $G$ in the case where

$B$ is division.

## Regularized theta lifts of integral weight harmonic Maass forms I

In these two talks we will give an overview on developments in the theory of regularized theta lifts

of harmonic Maass forms of integral weight. In particular, we report on recent work which extends

the Shintani theta lift to harmonic Maass forms. This yields interesting number theoretic applications.

## Regularized theta lifts of integral weight harmonic Maass forms II

In these two talks we will give an overview on developments in the theory of regularized theta lifts

of harmonic Maass forms of integral weight. In particular, we report on recent work which extends

the Shintani theta lift to harmonic Maass forms. This yields interesting number theoretic applications.