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Upcoming Talks

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

Recent developments in Quantum Topology -- Cancelled --

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We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

IMPRS seminar on various topics: single talk

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Date: 
Tue, 16/04/2024 - 10:00 - Tue, 06/08/2024 - 11:30
Location: 
MPIM Lecture Hall
Details: 
Program and Abstracts of IMPRS seminar on various topics: single talk

tba [SAG Seminar]

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Speaker: 
Fabian Reede
Affiliation: 
Hannover
Date: 
Thu, 02/05/2024 - 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar Algebraic Geometry (SAG)

Organizational Meeting for the Summer Term [Math-Phys Seminar]

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Speaker: 
David Aretz and David Prinz
Date: 
Thu, 02/05/2024 - 12:00 - 13:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Math-Phys Seminar

 

We discuss the schedule for the summer term: Please think of topics that you would like to discuss in the group and a talk that you could present.

Lie groupoids determined by their orbit spaces

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Speaker: 
David Miyamoto
Affiliation: 
MPIM
Date: 
Thu, 02/05/2024 - 13:45 - 14:45
Location: 
MPIM Lecture Hall
Parent event: 
Workshop "Higher Geometric Structures along the Lower Rhine XVII", May 2 - 3, 2024

he orbit space of a Lie groupoid carries a natural diffeology. More generally, we have a quotient functor from the Hilsum-Skandalis category of Lie groupoids to the category of diffeological spaces. We introduce a class of effective Lie groupoids, called "lift-complete," for which this functor restricts to an equivalence of distinguished sub-categories. In particular, the diffeomorphism class of the orbit space of a lift-complete Lie groupoid determines its Morita class.

Higher categorical structures in symplectic geometry

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Speaker: 
Katrin Wehrheim
Affiliation: 
UC Berkeley/MPIM
Date: 
Thu, 02/05/2024 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar
Parent event: 
Workshop "Higher Geometric Structures along the Lower Rhine XVII", May 2 - 3, 2024

We will explore higher categorical structures in symplectic geometry by taking some not entirely rigorous but everthemore instructive shortcuts to the algebraic implications of the analysis of pseudoholomorphic curves. Please come prepared to engage in collective inquiry on questions such as

  • Why do pseudoholomorphic disks generate $A_\infty$ algebras?
  • What is $A_\infty$ algebra anyways?
  • What 2- or $\infty$-categorical structures arise from interpreting string diagrams as pseudoholomorphic curves? 

The bending lamination conjecture for hyperbolic 3-manifolds [OS Differentialgeometrie]

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Speaker: 
Jean-Marc Schlenker
Affiliation: 
University of Luxembourg/MPIM
Date: 
Thu, 02/05/2024 - 16:30 - 18:00
Location: 
MPIM Seminar Room
Parent event: 
Oberseminar Differentialgeometrie

 

A quick proof of the étale and pro-étale exodromy theorems

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Speaker: 
Remy van Dobben de Bruyn
Affiliation: 
Utrecht
Date: 
Thu, 02/05/2024 - 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Workshop "Higher Geometric Structures along the Lower Rhine XVII", May 2 - 3, 2024

Locally constant sheaves are most easily understood as representations of the fundamental group, via the monodromy correspondence. In algebraic geometry, it is often preferable to use the larger class of constructible sheaves, as these are stable under (higher) pushforward. In 2018, Barwick, Glasman, and Haine proved an exodromy correspondence for constructible étale sheaves, using ideas from higher topos theory and profinite stratified homotopy theory.

Stability of fixed points of Dirac structures

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Speaker: 
Karandeep Singh
Affiliation: 
MPIM
Date: 
Fri, 03/05/2024 - 09:30 - 10:30
Location: 
MPIM Lecture Hall
Parent event: 
Workshop "Higher Geometric Structures along the Lower Rhine XVII", May 2 - 3, 2024

Given a geometric structure which induces a foliation on a manifold and a leaf of this foliation, one can ask when the leaf is preserved under deformations of the geometric structure. For Poisson structures and Lie algebroids, this question was addressed by Marius Crainic and Rui Loja Fernandes, and they showed that a leaf is stable when a certain cohomology group vanishes. I will give a general approach to such questions in terms of the L-infinity-algebra governing the deformations of the geometric structure, and an L-infinity-subalgebra.

A unified approach to different generalizations of $\infty$-category theory

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Speaker: 
Jaco Ruit
Affiliation: 
Utrecht
Date: 
Fri, 03/05/2024 - 11:00 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Workshop "Higher Geometric Structures along the Lower Rhine XVII", May 2 - 3, 2024

The language of Joyal and Lurie’s $\infty$-categories has now become indispensable in homotopy theory. However, for some purposes, it is convenient to pass to indexed or enriched versions of $\infty$-categories. For instance, homotopy theories of mathematical objects that admit symmetries governed by some group $G$, are usually better organized in so-called $G$-equivariant $\infty$-categories. We will see some examples of this principle. There are specialized notions of categorical concepts in the equivariant context, such as adjunctions, (co)limits, and Kan extensions.

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