# Abstracts for Higher Geometric Structures along the Lower Rhine XI, March 8-9, 2018

Alternatively have a look at the program.

## Periodic orbits and topological restriction homology

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Speaker:
Cary Malkiewich
Affiliation:
Binghampton University, New York/MPIM
Date:
Thu, 2018-03-08 13:45 - 14:45
Location:
MPIM Lecture Hall

I will talk about a project to import trace methods, usually reserved for algebraic K-theory computations, into the study of periodic orbits of continuous dynamical systems (and vice-versa). Our main result so far is that a certain fixed-point invariant built using equivariant spectra can be "unwound" into a more classical invariant that detects periodic orbits. As a simple consequence, periodic-point problems (i.e. finding a homotopy of a continuous map that removes its n-periodic orbits) can be reduced to equivariant fixed-point problems.

## Commutative cochain algebras

Posted in
Speaker:
Steffen Sagave
Affiliation:
Date:
Thu, 2018-03-08 15:00 - 16:00
Location:
MPIM Lecture Hall
Parent event:
MPI-Oberseminar

Homotopy coherent commutative multiplications on chain complexes of modules over a commutative ring can be encoded by the action of an $E$-infinity operad. Alternatively, one can model such $E$-infinity differential graded algebras by commutative $I$-dgas, which are strictly commutative objects in diagrams of chain complexes indexed by the category of finite sets and injections $I$. In this talk $I$ will explain how the cochain algebra of a space arises as a commutative $I$-dga in a natural way.

## Cohomology of higher categories

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Speaker:
Joost Nuiten
Affiliation:
Utrecht University
Date:
Thu, 2018-03-08 16:30 - 17:30
Location:
MPIM Lecture Hall

Classical obstruction theory studies the extensions of a continuous map along a relative CW-complex in terms of cohomology with local coefficients. In this talk, I will describe a similar obstruction theory for $(\infty, 1)$- and $(\infty, 2)$-categories, using cohomology with coefficients in local systems over the twisted arrow category and the `twisted 2-cell category'.  As an application, I will give an obstruction-theoretic argument that shows that adjunctions can be made homotopy coherent (as proven by Riehl–Verity). This is joint work with Yonatan Harpaz and Matan Prasma.

## Symmetries in shifted Poisson geometry and BV quantization

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Speaker:
Owen Gwilliam
Affiliation:
MPIM Bonn
Date:
Fri, 2018-03-09 09:30 - 10:30
Location:
MPIM Lecture Hall

The abstract structure of the Batalin-Vilkovisky formalism is nicely captured in operadic language, so that 1-shifted Poisson algebras encode the algebra of classical theories and BD algebras encode the algebra of quantum theories. We explain this language and then discuss what it means for a Lie algebra (or higher versions) to act on such algebras. Our primary aim is then to extract consequences at the level of factorization algebras for field theories.

## Ruled log-symplectic 4-manifolds

Posted in
Speaker:
Davide Alboresi
Organiser(s):
Utrecht University
Date:
Fri, 2018-03-09 11:00 - 12:00
Location:
MPIM Lecture Hall

In complex algebraic geometry, a ruled surface is a 2-dimensional projective variety such that there exists a (complex projective) line through each point. Symplectic ruled surfaces were studied by McDuff in the 90´s. In this talk, I will give a characterization of ruled surfaces in the log-symplectic category. The proof uses a construction of moduli spaces of holomorphic curves, which I will discuss.

## Anderson duality

Posted in
Speaker:
Lennart Meier
Affiliation:
Utrecht University
Date:
Fri, 2018-03-09 14:00 - 15:00
Location:
MPIM Lecture Hall

Anderson duality sends a spectrum to a spectrum with the "dual homotopy groups". This is a survey talk about recent computations and applications of Anderson duals.

## Derived brackets = hamiltonian flow

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Speaker:
Yael Fregier
Affiliation:
Université d'Artois, Arras/MPIM
Date:
Fri, 2018-03-09 15:30 - 16:30
Location:
MPIM Lecture Hall

Schlessinger and Stasheff have discovered in the 80's $L_\infty$-algebras. These algebras nowadays play an important rôle in many different areas, in particular via deformation theory. A very efficient tool to build such algebras is the derived bracket construction of T. Voronov. In this talk we will give a geometric interpretation of this construction

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