Topological Quantum Field Theory
Combinatorics in knot-quiver correspondences.
Marko Stošić, Instituto Superior Técnico.
13 seminars found
Combinatorics in knot-quiver correspondences.
Marko Stošić, Instituto Superior Técnico.
Quantization of Kähler manifolds.
Naichung Conan Leung, The Chinese University of Hong Kong.
I will explain recent work on relationships among geometric quantization, deformation quantization, Berezin-Toeplitz quantization and brane quantization.
Local constructions of exotic Lagrangian tori.
Joé Brendel, Université de Neuchâtel.
Certain simple symplectic manifolds (symplectic vector space, Milnor fibres of certain complex surface singularities,...) contain sets of symplectically distinct Lagrangian tori which have the following remarkable property: they remain symplectically distinct under embeddings into any reasonable (i.e. geometrically bounded) symplectic manifold. This leads to a vast extension of the class of spaces in which the existence of exotic tori is known, especially in dimensions six and above. In this talk we mainly focus on recent joint work with Johannes Hauber and Joel Schmitz which treats the more intricate case of dimension four.
Carroll Strings with an Extended Symmetry Algebra.
Watse Sybesma, University of Iceland & Isaac Newton Institute for Mathematical Sciences.
Starting from the Polyakov action we consider two distinct Carroll limits in target space, keeping the string worldsheet relativistic. The resulting magnetic and chiral Carroll string models exhibit different symmetries and dynamics. Both models have an in- finite dimensional symmetry algebra with Carroll symmetry included in a finite dimensional subalgebra. For the magnetic model, this is the so-called string Carroll algebra. The chiral model realises an extended version of the string Carroll algebra. The magnetic model does not have any transverse string excitations. The chiral model is less restrictive and includes arbitrary left-moving modes that carry transverse momentum but do not contribute to the energy in target space.
A universal coloured Alexander invariant from configurations on ovals in the disc.
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).
To be announced.
Adrien Brochier, Université Paris-cité.
Gambler’s ruin with three gamblers.
Persi Diaconis, Stanford University.
Imagine three gamblers with respectively $A$, $B$, $C$ at the start. Each time, a pair of gamblers are chosen (uniformly at random) and a fair coin is flipped. Of course, eventually, one of the gamblers is eliminated and the game continues with the remaining two until one winds up with all $A+B+C$. In poker tournaments (really) it is of interest to know the chances of the six possible elimination orders (e.g. $3,1,2$ means gambler $3$ is eliminated first, then gambler 1, leaving 2 with all the cash). In particular, how do these depend on $A,B,C$? For small $A,B,C$, exact computation is possible, but for $A,B,C$ of practical interest, asymptotics are needed. The math involved is surprising; Whitney and John domains, Carlesson estimates. To test your intuition, recall that if there are two gamblers with $1$ and $N-1$ the chance that the first winds up with all $N$ is $1/N$. With three gamblers with $1,1$ and $N-2$ the chance that the third is eliminated first is $\frac{\operatorname{Const}}{N^3}$. We don't know the answer for four gamblers. This is a report of joint work with Stew Ethier, Kelsey Huston-Edwards and Laurent Saloff-Coste.
To be announced.
Sebastian Schulz, Johns Hopkins University.
To be announced.
Inbar Klang, Vrije University Amsterdam.
To be announced.
Cécile Mercadier, Université Claude Bernard – Lyon 1, France.
To be announced.
Cécile Mercadier, Université Claude Bernard – Lyon 1, France.
To be announced.
Nils Carqueville, University of Vienna.
To be announced.
Diogo Oliveira e Silva, Instituto Superior Técnico.