Planned seminars

Europe/Lisbon

Cristina Anghel

, University of Leeds

The coloured Jones and Alexander polynomials are quantum invariants that come from representation theory. There are important open problems in quantum topology regarding their geometric information. Our goal is to describe these invariants from a topological viewpoint, as intersections between submanifolds in configuration spaces. We show that the Nth coloured Jones and Alexander polynomials of a knot can be read off from Lagrangian intersections in a fixed configuration space. At the asymptotic level, we geometrically construct a universal ADO invariant for links as a limit of invariants given by intersections in configuration spaces. The parallel question of providing an invariant unifying the coloured Jones invariants is the subject of the universal Habiro invariant for knots. The universal ADO invariant that we construct recovers all of the coloured Alexander invariants (in particular, the Alexander polynomial in the first term).

Europe/Lisbon Unusual schedule
Room P3.10, Mathematics Building Instituto Superior Técnicohttps://tecnico.ulisboa.pt

Jan-Willem van Ittersum

, University of Cologne

Starting with a counting problem for elements of the symmetric group, we introduce the so-called shifted symmetric functions. These functions, which also occur naturally in enumerative geometry, have the remarkable property that the corresponding generating series are quasimodular forms. We discuss another family of functions on partitions with the same property. In particular, using certain Hamiltonian operators associated to cohomological field theories, we explain how this seemingly different family of functions turns out to be closely related to the shifted symmetric functions.

Europe/Lisbon

Adrien Brochier

, Université Paris-cité
To be announced

Europe/Lisbon

Sebastian Schulz

, Johns Hopkins University
To be announced

Europe/Lisbon

Nils Carqueville

, University of Vienna
To be announced