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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
Zugehörigkeit: 
Binghampton University, New York/MPIM
Datum: 
Don, 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

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Speaker: 
Steffen Sagave
Zugehörigkeit: 
Radboud University, Nijmegen
Datum: 
Don, 2018-03-08 15:00 - 16:00
Location: 
MPIM Lecture Hall

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
Zugehörigkeit: 
Utrecht University
Datum: 
Don, 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
Zugehörigkeit: 
MPIM Bonn
Datum: 
Fre, 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

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Speaker: 
Davide Alboresi
Organiser(s): 
Utrecht University
Datum: 
Fre, 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

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Speaker: 
Lennart Meier
Zugehörigkeit: 
Utrecht University
Datum: 
Fre, 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
Zugehörigkeit: 
Université d'Artois, Arras/MPIM
Datum: 
Fre, 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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