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Upcoming Talks

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

Seminar on Kac-Moody algebras and related topics

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Organiser(s): 
Giovanni Faonte, Benjamin Hennion, Lin Weng
Date: 
Fri, 2017-02-10 13:30 - Sun, 2017-12-31 15:00
Location: 
MPIM Lecture Hall

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

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Speaker: 
Kenji Makiyama
Affiliation: 
Kyoto Sangyo University
Date: 
Thu, 2017-11-23 09:50 - 10:40
Location: 
MPIM Lecture Hall

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

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Speaker: 
Vladimir Guletskii
Affiliation: 
Liverpool
Date: 
Thu, 2017-11-23 10:30 - 12:00
Location: 
MPIM Seminar Room

Eisenstein and CM congruence modules defined over a real quadratic filed

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Speaker: 
Tomomi Ozawa
Affiliation: 
University Paris 13
Date: 
Thu, 2017-11-23 11:10 - 12:00
Location: 
MPIM Lecture Hall

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

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Speaker: 
Steffen Löbrich
Affiliation: 
University of Cologne
Date: 
Thu, 2017-11-23 12:10 - 12:50
Location: 
MPIM Lecture Hall

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

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Speaker: 
Sibasish Banerjee, Giordano Cotti, Mark Penney
Date: 
Thu, 2017-11-23 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Construction of vector valued Siegel modular forms and examples of congruences

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Speaker: 
Sho Takemori
Affiliation: 
MPIM
Date: 
Fri, 2017-11-24 09:50 - 10:40
Location: 
MPIM Lecture Hall

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

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Speaker: 
Hidetaka Kitayama
Affiliation: 
Wakayama University
Date: 
Fri, 2017-11-24 11:10 - 12:00
Location: 
MPIM Lecture Hall

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

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Speaker: 
Claudia Alfes-Neumann
Affiliation: 
University of Paderborn
Date: 
Fri, 2017-11-24 14:10 - 15:00
Location: 
MPIM Lecture Hall

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

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Speaker: 
Markus Schwagenscheidt
Affiliation: 
Technical University Darmstadt
Date: 
Fri, 2017-11-24 15:30 - 16:10
Location: 
MPIM Lecture Hall

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.

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