Abstracts for Higher Geometric Structures along the Lower Rhine VIII
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Hermitian K-theory and trace methods
Emanuele Dotto
MPIM Lecture Hall
Higher Geometric Structures along the Lower Rhine VIII
The Hermitian K-theory of a ring with anti-involution is the group-completion of its space of Hermitian forms and isometries. In recent work Hesselholt and Madsen describe this space as the $\mathbb{Z}/2$-fixed-points of an involution on the algebraic K-theory spectrum of the underlying ring. The geometric fixed-points of this $\mathbb{Z}/2$-spectrum are equivalent, at least when 2 is invertible, to the symmetric L-theory spectrum of the ring.
On Morita equivalence of pointed fusion categories
Bernardo Uribe
Universidad del Norte / MPIM
MPI-Oberseminar
Pointed fusion categories are characterized by a finite group and a 3-cocycle with values in U(1). In this talk I will show under which necessary and sufficient conditions two pointed fusion categories have equivalent categories of modules. Since Morita equivalent pointed fusion categories have isomorphic Drinfeld centers, we obtain as a byproduct isomorphic Drinfeld doubles associated to different groups and different 3-cocycles.
Homotopy theory of unital algebras
Brice le Grignou
In this talk, I will describe the homotopy theory of differential graded unital associative algebras. We already know that they are organized into a model category whose weak equivalences are quasi-isomorphisms. However, the computations of cofibrant resolutions of algebras make this framework unwieldy. I will show that the category of dg unital associative algebras may be embedded into the category of curved coalgebras whose homotopy theory is equivalent but more manageable. Then, I will generalize this method to the case of dg operads and to the case of algebras over an operad.
On the space of compact Poisson transversals
Ioan Marcut
Fri, 2016-12-16 09:30 - 10:30
The role of Poisson transversals in Poisson geometry is analogous to the one played by symplectic submanifolds in symplectic geometry, and by transverse submanifolds in foliation theory. They are defined as submanifolds that intersect the symplectic leaves transversally and symplectically. I will talk about the geometry of the infinite dimensional manifold of compact Poisson transversals; in particular, for unimodular Poisson structures, this space carries a symplectic structure. This is joint work with Pedro Frejlich.
Lie algebroids from higher Lie groupoids
Joost Nuiten
Recently there has been increasing interest in Lie n-groupoids, certain higher generalizations of Lie groupoids. One expects such objects to have (infinitesimal) linear counterparts in the form of Lie algebroids, but the construction of such algebroids tends to be quite complicated. In this talk I will describe a method for associating a Lie algebroid to a higher Lie groupoid by constructing a formal moduli problem, which in turn is classified by a Lie algebroid.
Correction terms in low dimensional topology
Stefan Behrens
Correction terms are numerical invariants of 3-manifolds that arise in the context of Heegaard-Floer and Seiberg-Witten theory. They have many applications in low dimensional toplogy, for example, they can be used to study intersection forms of smooth 4-manifolds with boundary. By varying the coefficients one obtains a plethora of correction terms whose relations are still poorly understood. I will report on recent work and thoughts on this issue.
Singular support of coherent sheaves
Pavel Safronov
Singular support of coherent sheaves was introduced by Arinkin and Gaitsgory in their work on the geometric Langlands conjecture. In this talk I will describe a categorification of the notion of differential operators via higher deformation quantization. In particular, I will explain how one can rediscover singular support of coherent sheaves as a straightforward categorification of the notion of singular support of distributions.
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