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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. I will further explain how this presentation was used to prove the P=W conjecture of de Cataldo-Hausel-Migliorini about the perverse filtration on the cohomology of the Hitchin system of a smooth projective curve C.

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. Continuing from an earlier joint work with Côté, Nadler, and Shende, we will globalize this correspondence to general complex contact manifolds in an upcoming work.

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. In this talk, I will describe a solution to an old conjecture of Franke that the arithmetic - topology correspondence can be refined to an equivalence of categories when the ambient prime is sufficiently large.

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. Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory, are invariants of (certain) 3-manifolds / fiber bundles / knots and links (it is the same argument in different settings). Watanabe's work implies that these invariants detect exotic phenomena, and, since then, they have become an important tool in studying the topology of diffeomorphism groups. It is thus natural to ask: how to understand the role smooth structure plays in Kontsevich's invariants? My recent work provides a perspective on this question: the real blow-up operations on a smooth manifold depend on the smooth structure in an essential way; thus, the topology of the spaces obtained by doing some blow-ups on a smooth manifold/fiber bundle X encodes information of the smooth structure on X.

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. Floer applied this idea in the infinite dimensional setting to produce new invariants in symplectic and low dimensional topology, and motivated by this, Cohen, Jones and Segal has shown how to obtain finer information about the topology of a smooth manifold from the Morse theory, thus providing a framework for refining Floer's invariant too. However, neither Morse theory nor the framework of Cohen-Jones-Segal are compatible with the compact group actions on the underlying manifold. In this talk, I will explain how to define a new framework for Morse-Bott functions in order to extract information about the equivariant stable homotopy type. In the remaining time, I will discuss applications to equivariant Floer theory. Joint work with Laurent Coté.

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


https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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



https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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


https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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



https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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


https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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



https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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


https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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



https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09
Code: 069444

Lecture webpage:

https://indico.math.cnrs.fr/event/10347/
 

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)

We will embark on a case study of two exotically knotted surfaces in the 4-ball (with boundary in the 3-sphere) that arise from the "atomic approach" to Wall-type stabilization problems. I will sketch the arguments that show these two surfaces are topologically isotopic yet are not smoothly isotopic and, moreover, remain smoothly distinct after "internally" stabilizing via connected sum with T2. The key obstruction comes from the universal version of Khovanov homology and builds on prior joint work with Sundberg. Time permitting, I will discuss a speculative approach for using the spectral sequence from Khovanov homology to monopole Floer homology to study the branched double covers of these surfaces, which are exotic 4-manifolds that are candidates to remain exotic after connected sum with S2xS2.

 

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