Higher Structures Day

Université Paris 13, Laboratoire Analyse, Géométrie et Applications (LAGA), June 21, 2018

A special day of the seminar of the Algebraic Topology team will be devoted to the topic of Higher Structures with talks of the members of the PhD jury of the thesis of Daniel Robert-Nicoud (June 22). 



The talks will take place at Amphitheater Fermat of the Institute Galilée (Villetaneuse Campus). Indications here (French) and there (English)


Everybody is of course welcome. However, in order to organize the coffee breaks and the lunch, a quick email to Bruno Vallette will be appreciated.

Titles and abstracts:   

Abstract: I will talk about work in progress on understanding the rational homotopy type of BDiff(M) for simply connected manifolds M.
By combining earlier work of Madsen and myself with classical work on pseudo-isotopy theory and algebraic K-theory of spaces, due to Waldhausen, Burghelea--Lashof, Dwyer--Hsiang--Staffeldt and others, we construct a dg Lie algebra that encodes the rational homotopy type of BDiff(M) in the so-called pseudo-isotopy stable range.
Abstract: I will give a sheaf-theoretic description of the E-infinity structure carried by the singular cochain complex of every reasonable topological space. I will then discuss some applications to the study of Steenrod operations associated to algebraic varieties (via the weight filtration) and to singular spaces (via intersection cohomology). This is joint work in progress with David Chataur.
Abstract: The little n-disks operads are classical objects in topology, introduced by Boardman-Vogt and May in the 1970's in their study of iterated loop spaces. They have since seen a wealth of applications in algebra and topology, and received much attention recently due to their appearance in the manifold calculus of Goodwillie and Weiss, and relatedly in the factorization (or topological chiral) homology by Lurie, Francis, Beilinson-Drinfeld and others.
I report on joint work with Victor Turchin and Benoit Fresse, in which we (mostly) settle the rational homotopy theory of the little n-disks operads, by showing that they are intrinsically formal for n>=3, and by computing the rational homotopy type of the function spaces between these objects.
As an application we obtain complete rational invariants of long knots in codimension >=3.
Abstract: Nekrasov's partition functions of N=2 supersymmetric gauge theories are generating series of integrals of equivariant cohomology or K-theory classes on instanton moduli spaces for all instanton numbers. They also arise in conformal field theory and derived representation schemes, and have a representation as random matrix integrals. I will review these relations and present recent results obtained with Martin Müller-Lennert on the radius of convergence of Nekrasov's partition functions and Whittaker vectors for the q-Virasoro algebra.

Related event:  

The defence of the PhD thesis of Daniel Robert-Nicoud on the topic of "Operads and Maurer--Cartan spaces" will take place on June 22nd (2pm) at the Amphitheater Euler of the Institute Galilée.

Last update: June 8nd, 2018.