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Titles and abstracts

Larry Breen
Group laws on higher categories
A functorial description of the cohomology of Eilenberg-Mac Lane spaces K(A,n) provides some insight into the structure of group laws on higher categories as well as to the description of such categories. I will illustrate this with examples in low degrees and discuss its relevance to related fields, in particular to topological quantum field theory. I will also present some recent results from joint work with Roman Mikhailov and Antoine Touzé in which we functorially compute the integral homology groups H_i(K(A,n)) for a free abelian group A, for a larger range of values of the pair of integers (n,i) than previously known.

Yonatan Harpaz
Model fibrations and the Grothendieck correspondence for model categories
A classical theorem of Grothendieck asserts that the notion of a pseudo-functor F: C \to Cat can be modeled by a suitable fibration of categories D \to C, yielding an equivalence between the associated
2-categories. This more geometric manifestation of F proved extremely useful in many situations, and admits powerful generalizations to the setting of higher category theory. In this lecture, we will discuss an
analogous equivalence in the world of model categories. Given a certain model theoretic structure on a category M, we will explain how to encode a suitable notion of a pseudo-functor M \to ModCat via a new natural notion of a model fibration N \to M, yielding an equivalence between the associated (2,1)-categories. Some potential applications will be considered. This is joint work with Matan Prasma.

Ralph Kaufmann
A 2-categorical interpretation of Hochschild actions and string topology
We provide a cobordism 2-category that gives a model for moduli spaces of curves with marked points and an arbitrary number of tangent vectors at each point. This can be augmented by adding certain operad-like structures. In the particular case of one tangent vector at each marked point, there is a natural action on Hochschild complexes, which recovers our algebraic string topology action. In this version, we can see why this action is in a precise version,a free action of a (co)bar transform. This is joint work with Chris Schommer-Pries and Yu Tsumura.

Pascal Lambrechts
Cosimplicial models for spaces of smooth embeddings
In this talk I will recall how Goodwillie-Klein-Weiss theory can be used to understand the space of smooth embeddings of a given compact manifold M into another manifold W. I will show how we can actually give a very simple cosimplicial model of the space Emb(M,W) out of simplicial model of M. I will also explain consequences of this on the rationnal homology of these embedding spaces. This is a joint work with Greg Arone and Daniel Pryor.

Silvia Sabatini
Using number theory for counting the number of fixed points of periodic flows
In this talk I will explain how to count the number of fixed points of a circle action on a compact almost complex manifold M of dimension 2n with nonempty fixed point set, provided the Chern number c_1c_{n-1}[M] vanishes. The proof combines techniques originating in equivariant K-theory with number theory results on polygonal numbers, introduced by Pierre de Fermat. Our results apply, for example, to a class of manifolds which do not support any Hamiltonian circle action, namely those for which the first Chern class is torsion. This includes, for instance, all symplectic Calabi Yau manifolds. This is joint work with L. Godinho and A. Pelayo. arXiv:1404.4541 [math.AT]

Urs Schreiber
Generalized differential cohomology and quantization
I review the recent "cohesive" solution to the problem of characterizing and constructing generalized differential cohomology theories (section 4.1.2.2 of arXiv:1310.7930). Applied to supergeometry this produces higher super-gerbes with connection, and I discuss how these provide a differential model for the geometric twists of K-theory and of tmf (section 4.6). I close by indicating how the higher prequantum geometry over these coefficients (section 3.9.13) solves quantum-anomaly cancellation problems in the quantization of superstrings (arXiv:1402.7041).

Daniele Sepe
Isotropic realisations of Jacobi manifolds
Jacobi manifolds, introduced by Lichnerowicz and Kirillov independently, are analogous (while at the same time generalising) Poisson manifolds, in the sense that the role of symplectic geometry in the latter is played by contact manifolds in the former. Recent work of Crainic and Salazar has provided a new geometric approach to studying Jacobi structures defined on any real line bundle, i.e. not necessarily trivial. Motivated by the theory of integrable Hamiltonian systems on contact manifolds, as well as by the idea of exploring `compactness' in Jacobi manifolds (analogous to that which Crainic, Fernandes and Martínez-Torres introduced for their Poisson counterparts), this talk presents the classification of some special types of `desingularisations' of Jacobi structures, which are analogous to those studied by Dazord and Delzant in the Poisson domain. This is joint work with M. A. Salazar.