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

Infinitesimal categorical Torelli: an application to Kuznetsov' Fano 3-folds conjecture

Posted in
Speaker: 
Xun Lin
Affiliation: 
MPIM
Date: 
Thu, 21/12/2023 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

In this talk, we introduce the infinitesimal categorical Torelli for Fano 3-folds. We obtain a commutative diagram connecting the infinitesimal spaces
of the geometric spaces and the categories. These are joint works with Jacovskis Augustinas, Zhiyu Liu, and Shizhuo Zhang. In a joint work with
Shizhuo Zhang, we give a simple new disproof of Kuznetsov's Fano 3-folds conjecture for degree 2 and index two Fano 3-fold based on infinitesimal
categorical Torelli theorems.

Semi-infinite t-structures via hyperbolic localization

Posted in
Speaker: 
Andreas Hayash
Affiliation: 
MPIM
Date: 
Tue, 12/12/2023 - 15:05 - 16:50
Location: 
MPIM Lecture Hall

For any nice enough scheme with an action of the multiplicative group it is possible to define a t-structure on a certain category of monodromic D-modules using hyperbolic localization. I will discuss the construction of these t-structures as well as an application to geometric representation theory. Specifically, I will explain how the semi-infinite IC sheaf associated to a semisimple group arises as an intermediate extension in this t-structure for Drinfeld's Zastava spaces.
 

Cohomological Hall algebras and P=W conjecture

Posted in
Speaker: 
Alexandre Minets
Affiliation: 
University of Edinburgh/MPIM
Date: 
Thu, 14/12/2023 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Let S be a smooth surface, and Coh(S) the moduli stack of properly supported coherent sheaves on S. One can equip the Borel-Moore homology of Coh(S) with a convolution algebra structure; this is called the cohomological Hall algebra (CoHA) of S. While understanding CoHA algebraically is more or less hopeless for a general S, I will give an explicit presentation of its part, which corresponds to sheaves with zero-dimensional support.

The tail of the colored Jones polynomial for arborescent knots

Posted in
Speaker: 
Matthias Storzer
Affiliation: 
MPIM/Universität Bonn
Date: 
Tue, 12/12/2023 - 10:15 - 11:45
Location: 
MPIM Lecture Hall

Microlocal Riemann-Hilbert correspondence

Posted in
Speaker: 
Christopher Kuo
Affiliation: 
USC Dornsife
Date: 
Tue, 12/12/2023 - 13:30 - 14:30
Location: 
MPIM Lecture Hall

For complex manifolds, the Riemann-Hilbert correspondence generalizes the classical correspondence between finite dimensional local systems and D-modules which are coherent as O-modules to perverse sheaves and regular holonomic D-modules. These later objects are in fact microlocal in nature that they can be regarded as living on the cotangent bundles, and the correspondence admits a microlocalization as well.

How algebraic is space?

Posted in
Speaker: 
Piotr Pstrągowski
Affiliation: 
Harvard
Date: 
Fri, 15/12/2023 - 16:00 - 17:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

A phenomena in topology is said to be stable if it occurs in all sufficiently high dimensions. As discovered by Quillen over five decades ago, such phenomena are closely related to number theory, and can often be described in terms of arithmetic objects known as formal groups. Unfortunately, in general this dictionary is not quite a one-to-one and many periodicities one sees on the arithmetic side become broken and more complex in the world of topology.

Why can Kontsevich's invariants detect exotic phenomena?

Posted in
Speaker: 
Xujia Chen
Affiliation: 
Harvard
Date: 
Fri, 15/12/2023 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

In topology, the difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". The recent work of Watanabe (2018) uses the tool "Kontsevich's invariants" to show that the group of diffeomorphisms of the 4-dimensional ball, as a topological group, has non-trivial homotopy type. In contrast, the group of homeomorphisms of the 4-dimensional ball is contractible.

Analytic geometry and p-adic automorphic forms

Posted in
Speaker: 
Juan Esteban Rodriguez Camargo
Affiliation: 
Columbia University
Date: 
Thu, 14/12/2023 - 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

A Morse-Bott approach to the equivariant homotopy type

Posted in
Speaker: 
Yusuf Barış Kartal
Affiliation: 
University of Edinburgh
Date: 
Thu, 14/12/2023 - 11:00 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

Morse theory provides an effective way to calculate the homology of smooth manifolds, in terms of critical points of a function and its gradient flow.

Infinite discrete groups: geometry, analysis and probability

Posted in
Speaker: 
Maria Gerasimova
Affiliation: 
Universität Münster
Date: 
Thu, 14/12/2023 - 09:00 - 10:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

Analytic Stacks

Posted in
Speaker: 
Peter Scholze
Affiliation: 
MPIM
Date: 
Fri, 09/02/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Dustin Clausen
Affiliation: 
IHES
Date: 
Wed, 07/02/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Peter Scholze
Affiliation: 
MPIM
Date: 
Fri, 02/02/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Dustin Clausen
Affiliation: 
IHES
Date: 
Wed, 31/01/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Peter Scholze
Affiliation: 
MPIM
Date: 
Fri, 26/01/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Dustin Clausen
Affiliation: 
IHES
Date: 
Wed, 24/01/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Peter Scholze
Affiliation: 
MPIM
Date: 
Fri, 19/01/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Analytic Stacks

Posted in
Speaker: 
Dustin Clausen
Affiliation: 
IHES
Date: 
Wed, 17/01/2024 - 10:15 - 12:00
Location: 
MPIM Lecture Hall

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.
Lectures will be given by Dustin Clausen at IHES and Peter Scholze at MPI, and broadcast live at the other location.
We also plan to make the lectures accessible by Zoom, and record them.

Mi, 10(c.t.) - 12 Uhr, und Fr, 10(c.t.) - 12 Uhr, MPI-Hörsaal

Selected Topics in Differential Geometry - The classical Plateau Problem

Posted in
Speaker: 
Stephan Stadler
Affiliation: 
MPIM
Date: 
Thu, 14/12/2023 - 08:30 - 10:00
Location: 
MPIM Seminar Room

Stably exotic surfaces and Khovanov homology

Posted in
Speaker: 
Kyle Hayden
Affiliation: 
Rutgers Newark
Date: 
Tue, 12/12/2023 - 17:00 - 18:00
Location: 
MPIM Lecture Hall

(Virtual)

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