# Abstracts for Higher Geometric Structures along the Lower Rhine XIV, March 12 - 13, 2020

Alternatively have a look at the program.

## Rational commutative ring $G$-spectra

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Speaker:
Magdalena Kedziorek
Affiliation:
Nijmegen
Date:
Thu, 12/03/2020 - 13:45 - 14:45
Location:
MPIM Lecture Hall

The category of $G$-spectra, for any compact Lie group $G$ is very interesting, but at the same time very complicated. A big part of the interesting information comes from the internally encoded group action while one of the main complications comes from working over the integers. The first step in our understanding is to simplify this category by working over rationals. This removes the complexity coming from ordinary stable homotopy theory, while leaving much of the information about the group $G$.

## Integration of (higher) algebroids, (higher) principal bundles with connection and (higher) differential characters

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Speaker:
Rui Fernandes
Affiliation:
University of Illinois, Urbana-Champaign
Date:
Thu, 12/03/2020 - 15:00 - 16:00
Location:
MPIM Lecture Hall

I will discuss the correspondence between differential characters and higher principal $S^1$-bundles with connection, via the integration of Lie algebroids. The main point of the talk is that one needs to consider an "homological" integration, different from the standard "homotopic" integration. This is true already for ordinary principal $S^1$-bundles where the relevant integration is the so called genus integration of the prequantum algebroid, introduced in joint work with Contreras.

## Global group laws and the equivariant Quillen theorem

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Speaker:
Markus Hausmann
Affiliation:
Uni Bonn
Date:
Thu, 12/03/2020 - 16:30 - 17:30
Location:
MPIM Lecture Hall

Quillen's theorem that the complex bordism ring carries the universal formal group law is a fundamental result in stable homotopy theory. In this talk I will discuss equivariant versions of this result, both over a fixed abelian compact Lie group and in a global equivariant/stack setting.

## Conference dinner

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Date:
Thu, 12/03/2020 - 18:00 - 21:00

DelikArt Bonn

## Open discussion

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Date:
Thu, 12/03/2020 - 21:00 - 22:00
Location:
MPIM Lecture Hall

## Koszul duality and deformation theory

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Speaker:
Andrey Lazarev
Affiliation:
Lancaster/MPIM
Date:
Fri, 13/03/2020 - 09:30 - 10:30
Location:
MPIM Lecture Hall

Koszul duality between Lie algebras and cocommutative coalgebras constructed by Hinich is the basis for formal deformation theory, at least in characteristic zero.  In this talk I explain, following Manetti, Pridham and Lurie, how Koszul duality, combined with Brown representability theorem from homotopy theory leads to representability of a formal deformation functor up to homotopy. Sometimes a formal deformation functor has a `noncommutative structure', meaning that it is defined on a suitable homotopy category of associative algebras.

## Approximating foliations by contact structures

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Speaker:
Lauran Toussaint
Affiliation:
Utrecht
Date:
Fri, 13/03/2020 - 11:00 - 12:00
Location:
MPIM Lecture Hall

Although their definitions are in some sense opposite, contact structures and foliations display many similarities. This is especially clear in the $3$-dimensional theory of confoliations which unites both structures in a single framework. A famous theorem by Eliashberg and Thurston states that, with a single exception ($\mathbb{S}^1 \times \mathbb{S}^2$ foliated by spheres), any (con)foliation on a $3$-manifold can be approximated by contact structures.

## The Poisson cohomology of $\mathrm{sl}_2(\mathbb{C})$

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Speaker:
Florian Zeiser
Affiliation:
Nijmegen
Date:
Fri, 13/03/2020 - 14:00 - 15:00
Location:
MPIM Lecture Hall

To a Poisson manifold $(M,\pi)$ one can naturally associated a cohomology called Poisson cohomology. Although Poisson cohomology is important for questions such as linearization and deformations of poisson structures, it is in general quite difficult to compute. In this talk we look at the Poisson structure on the dual of a Lie algebra $(g, [~,~])$. We look at the relation of Poisson cohomology with the linearization problem and outline the general ideas behind the calculations for the case of $\mathrm{sl}_2(\mathbb{C})$. This is based on joint work with Ioan Marcut.

## Models of Lubin-Tate spectra via real bordism theory

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Speaker:
Mingcong Zeng
Affiliation:
Utrecht
Date:
Fri, 13/03/2020 - 15:30 - 16:30
Location:
MPIM Lecture Hall

In this talk, I will present models of Lubin-Tate theories at $p=2$ and all heights. These models come with explicit formulas for some finite subgroups of the Morava stabilizer groups on the coefficient rings. The construction utilizes equivariant formal group laws and are based on techniques of Hill-Hopkins-Ravenel. I will also talk about implications of the theorem, such as periodicity and differentials in spectral sequences. This is joint work with Beaudry, Hill and Shi.

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