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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 57R56 4 results

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Differential equation for the Reidemeister torsion - Marché, Julien (Author of the conference) | CIRM H

Post-edited

The Reidemeister torsion may be viewed as a volume form on the character variety of a 3-manifold with boundary. I will explain a conjectural differential equation that this form should satisfy, motivated by the study of the asymptotical behaviour of quantum invariants.

53D50 ; 57M25 ; 57M27 ; 57R56

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2y

The Verlinde formula for Higgs bundles - Andersen, Jorgen Ellegaard (Author of the conference) | CIRM H

Post-edited

In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will explain how all these dimensions fit into a one parameter family of 2D TQFT's, encoded in a one parameter family of Frobenius algebras, which we will construct.

14D20 ; 14H60 ; 57R56 ; 81T40 ; 14F05 ; 14H10 ; 22E46 ; 81T45

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Surprising VOA structures from Quantum Topology - Gukov, Sergei (Author of the conference) | CIRM H

Multi angle

In quantum topology, one usually constructs invariants of knots and 3-manifolds starting with an algebraic structure with suitable properties that can encode braiding and surgery operations in three dimensions. ln this talk, 1 review recent work on q-series invariants of 3-manifolds, associated with quantum groups at generic q, that provide a connection between quantum topology and algebra going in the opposite direction: starting with a 3-manifold and a choice of Spin-C structure, the q-series invariant turns out to be a character of a (logarithmic) vertex algebra that depends on the 3-manifold. [-]
In quantum topology, one usually constructs invariants of knots and 3-manifolds starting with an algebraic structure with suitable properties that can encode braiding and surgery operations in three dimensions. ln this talk, 1 review recent work on q-series invariants of 3-manifolds, associated with quantum groups at generic q, that provide a connection between quantum topology and algebra going in the opposite direction: starting with a ...[+]

17B69 ; 57R56 ; 57M27 ; 58B32

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Complex hyperbolic structures on moduli spaces of curves and Fibonacci TQFT - Marché, Julien (Author of the conference) | CIRM H

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The Fibonacci TQFT gives interesting representations of mapping class groups into pseudo-unitary groups. In some exceptional cases, they correspond to holonomy representation of complex hyperbolic structures on some compactifications of the moduli spaces of curves. The proof uses a computation of the Toledo invariant which fits in the framework of Cohomological Field theories. This is joint work with Bertrand Deroin.

14D22 ; 53C10 ; 57R56

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