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
Titles and abstracts:
- Alexander Berglund: ``Differential graded Lie algebra models for diffeomorphism groups''
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.
- Joana Cirici: ``Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces''
: 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.
- Thomas Willwacher: ``Little disks operads and rational Goodwillie-Weiss calculus''
: 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
As an application we obtain complete rational invariants of long knots in codimension >=3.
- Giovanni Felder: ``Gauge theory partition functions, representation schemes and random matrices''
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.
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,