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Talk

Talks and seminars, possibly part of a conference or series.

New guests at the MPIM

Posted in
Speaker: 
Jian Zhang, Laura Pertusi
Date: 
Thu, 2019-03-28 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

tba

Posted in
Date: 
Fri, 2019-03-29 15:30 - 16:30
Location: 
MPIM Lecture Hall
Parent event: 
"What is...?" seminar

tba

Posted in
Date: 
Fri, 2019-03-29 14:15 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
"What is...?" seminar

tba

Posted in
Date: 
Fri, 2019-03-29 13:00 - 14:00
Location: 
MPIM Lecture Hall
Parent event: 
"What is...?" seminar

A short survey of Prismatic Cohomology (after P. Scholze and B. Bhatt), II

Posted in
Speaker: 
Alexei Pantchichkine
Affiliation: 
University Grenoble Alpes/MPIM
Date: 
Tue, 2019-04-02 14:00 - 15:00
Location: 
MPIM Lecture Hall

We will discuss the recently suggested definition of prismatic cohomology that unifies several integral cohomology theories in p-adic geometry. We briefly start with an introduction of prisms as generalization of perfectoid rings, and then describe available constructions of a prismatic site:

1) a variant of the complex $\Delta_{R/A}$$ (2016);
2) construction via topological Hochschild homology (2018).

It requires as input a highly non-trivial calculation from homotopy theory
due to Bockstedt.

A short survey of Prismatic Cohomology (after P. Scholze and B. Bhatt), I

Posted in
Speaker: 
Arnab Saha
Affiliation: 
MPIM
Date: 
Tue, 2019-03-26 14:00 - 15:00
Location: 
MPIM Lecture Hall

This is the first of the two talks that will be given in this seminar. It is an attempt to understand the work of
Bhargav Bhatt and Peter Scholze.  We will discuss the motivations and give an overview of p-adic Hodge
theory. In the process, we will introduce some of the basic notions such as delta-rings, Witt vectors, 
prisms and prismatic site.
 


 

tba

Posted in
Speaker: 
Sigmundur Gudmundsson
Affiliation: 
Lund University
Date: 
Thu, 2019-07-18 16:30 - 17:30
Location: 
MPIM Lecture Hall

tba

Posted in
Speaker: 
Charles Frances
Affiliation: 
Université de Strasbourg
Date: 
Thu, 2019-05-23 16:30 - 17:30
Location: 
MPIM Lecture Hall

Lower bounds for Mahler measure that depend on the number of monomials

Posted in
Speaker: 
Jeffrey Vaaler
Affiliation: 
The University of Texas at Austin
Date: 
Thu, 2019-04-04 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We prove a new lower bound for the Mahler measure of a polynomial in one and
in several variables that depends on the complex coefficients and the number of
monomials, but  not  on the degree. In one variable the lower bound generalizes a
classical inequality of Mahler. In M variables the inequality depends on Z^M as an
ordered group, and in general the lower bound depends on the choice of ordering. In
one variable the proof is elementary. In M variables the proof exploits an idea used
in earlier work of D. Boyd. The talk should be accessible to a general mathematical
audience. This is joint work with S. Akhtari.

tba

Posted in
Speaker: 
Martin Widmer
Affiliation: 
Royal Holloway, University of London
Date: 
Wed, 2019-04-03 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

tba

Posted in
Speaker: 
Ryan Blair
Affiliation: 
California State University, Long Beach
Date: 
Mon, 2019-04-01 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Translation surfaces of infinite-type, IV

Posted in
Speaker: 
Vincent Delecroix
Affiliation: 
Université Bordeaux 1/MPIM
Date: 
Tue, 2019-05-14 10:00 - 12:30
Location: 
MPIM Lecture Hall

Compact translation surfaces are intimately linked to the geometry
of Teichmüller spaces and the billiard dynamics in rational polygons.
During this is two week mini-course (4 x 2h30) our aim is to introduce
translation surfaces of infinite type (that is non-compact) both through
geometric and dynamical points of view.

We will first present several examples that motivate the study of
translation surfaces of infinite type, in particular several models
of billiards. The next lectures will go through the topological,
geometrical and dynamical properties of these examples.

Translation surfaces of infinite-type, III

Posted in
Speaker: 
Vincent Delecroix
Affiliation: 
Université Bordeaux 1/MPIM
Date: 
Mon, 2019-05-13 10:00 - 12:30
Location: 
MPIM Lecture Hall

Compact translation surfaces are intimately linked to the geometry
of Teichmüller spaces and the billiard dynamics in rational polygons.
During this is two week mini-course (4 x 2h30) our aim is to introduce
translation surfaces of infinite type (that is non-compact) both through
geometric and dynamical points of view.

We will first present several examples that motivate the study of
translation surfaces of infinite type, in particular several models
of billiards. The next lectures will go through the topological,
geometrical and dynamical properties of these examples.

Translation surfaces of infinite-type, II

Posted in
Speaker: 
Ferrán Valdez
Affiliation: 
Universidad Nacional Autónoma de México (UNAM)/MPIM
Date: 
Tue, 2019-05-07 10:00 - 12:30
Location: 
MPIM Lecture Hall

Compact translation surfaces are intimately linked to the geometry
of Teichmüller spaces and the billiard dynamics in rational polygons.
During this is two week mini-course (4 x 2h30) our aim is to introduce
translation surfaces of infinite type (that is non-compact) both through
geometric and dynamical points of view.

We will first present several examples that motivate the study of
translation surfaces of infinite type, in particular several models
of billiards. The next lectures will go through the topological,
geometrical and dynamical properties of these examples.

Translation surfaces of infinite-type, I

Posted in
Speaker: 
Ferrán Valdez
Affiliation: 
Universidad Nacional Autónoma de México (UNAM)/MPIM
Date: 
Mon, 2019-05-06 10:00 - 12:30
Location: 
MPIM Lecture Hall

Compact translation surfaces are intimately linked to the geometry
of Teichmüller spaces and the billiard dynamics in rational polygons.
During this is two week mini-course (4 x 2h30) our aim is to introduce
translation surfaces of infinite type (that is non-compact) both through
geometric and dynamical points of view.

We will first present several examples that motivate the study of
translation surfaces of infinite type, in particular several models
of billiards. The next lectures will go through the topological,
geometrical and dynamical properties of these examples.

Fundamental groups and rational points

Posted in
Speaker: 
Alexander Betts
Affiliation: 
MPIM
Date: 
Thu, 2019-03-21 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Colloquium
Parent event: 
MPI-Oberseminar

One powerful tool in the study of rational solutions to equations comes from various theories of fundamental groups of varieties, most notably the etale fundamental group developed by Alexander Grothendieck. In this talk, we will outline how one can apply such algebro-topological tools to the determination of solutions to equations, both in terms of Grothendieck's famous Section Conjecture and (time permitting) the non-abelian Chabauty method of Minhyong Kim. There will be a focus on providing a general overview of the area, illustrated by examples, rather than setting out precise definitions, and we hope the talk should be widely accessible.

tba

Posted in
Speaker: 
James Farre
Affiliation: 
University of Utah
Date: 
Mon, 2019-04-15 16:30 - 17:30
Location: 
MPIM Seminar Room

Homogeneous spaces, algebraic K-theory and cohomological dimension of fields

Posted in
Speaker: 
Diego Izquierdo
Affiliation: 
École Normale Supérieure Paris/MPIM
Date: 
Wed, 2019-03-20 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

In 1986, Kato and Kuzumaki stated a set of conjectures which aimed at giving a Diophantine characterization of the cohomological dimension of fields in terms of Milnor K-theory and points on projective hypersurfaces of small degree. Those conjectures are known to be wrong in general.
In this talk, we will prove a variant of Kato and Kuzumaki's conjectures in which projective hypersurfaces of small degree are replaced by homogeneous spaces. This is joint work with Giancarlo Lucchini Arteche.

New guests at the MPIM

Posted in
Speaker: 
Arnab Saha, Riccardo Iraso
Date: 
Thu, 2019-03-14 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Integral structure of vector-valued Siegel modular forms

Posted in
Speaker: 
Siegfried Böcherer
Affiliation: 
Universität Mannheim
Date: 
Wed, 2019-03-20 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We show how one can obtain almost all vector-valued Siegel modular forms from scalar-valued ones of higher degree by using appropriate differential operators, more precisely, only Siegel type Eisenstein series are needed in this procedure. In this way, one gets an integral structure on vector-valued modular forms from a classical result on rational Fourier coefficients (with bounded denominators) of such Eisenstein series. This procedure works for arbitrary congruence subgroups. We also report on applications of this result in the theory of p-adic vector-valued modular forms.

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