Categorification and applications
This workshop aims at highlighting recent applications of categorification in nearby fields and at presenting topics where the now classical categorification techniques could be used in the next few years.
|9:30 - 10:30
|10:30 - 11:00
|11:00 - 12:00
|12:00 - 14:00
|14:00 - 15:00
|15:00 - 15:30
|15:30 - 16:30
Zsuzsanna Dancso: The topological Duflo isomorphism
The Duflo isomorphism in Lie theory is an isomorphism between the invariant part of the symmetric algebra of a given Lie algebra, and the centre of its universal enveloping algebra. In 2003, Bar-Natan, Le and Thurston gave a topological proof for metrised Lie algebras. In this talk we give a topological proof in the general case, using a universal finite type invariant for certain knotted tubes in R^4, constructed recently by Bar-Natan and the speaker. If time allows, we'll discuss the broader connection to Lie theory: the (topological) Kashiwara-Vergne problem. (Joint work with Dror Bar-Natan.)
Clément Dupont: Arrangements of hypersurfaces, purity and formality
Arrangements of hypersurfaces are geometric objects which locally look like arrangements of hyperplanes, and generalize normal crossing divisors. Their study is a global version of the classical study of arrangements of hyperplanes, due to Arnold, Brieskorn and Orlik—Solomon, and mixes geometry with combinatorics. In this talk we will introduce tools to study cohomology groups associated to arrangements of hypersurfaces, and prove formality results.
Stephen Morgan: W-algebras and quantum Hamiltonian reduction by stages
We'll examine a branch of algebra which lies at the intersection of Lie theory, Poisson geometry and category theory. W-algebras are related to universal enveloping algebras, and like them carry a lot of information about the representation theory of the corresponding Lie algebras. In particular, the representation theory of W-algebras is closely related to the block decomposition of the BGG category O. We'll discuss how the geometry of the nilpotent cone and a quantum version of Hamiltonian reduction by stages can be used to relate different W-algebras.
Philippe Roche: Zeta function representations and 2-dimensional topological field theory: the case of p-adic groups
We recall the relation between Zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. The one point correlations functions are completely fixed by the knowledge of characters of the group. In the case of SU(2) it is related to Bernouilli polynomials. We analyze the p-adic case GL(2, O) where O is the ring of integers of a p-adic field.