PIRSA:C17001 - Hitchin Systems in Mathematics and PhysicsPODCAST Subscribe to podcast

Hitchin Systems in Mathematics and Physics


Collection URL: http://pirsa.org/C17001

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PIRSA:17020017  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Critical points and spectral curves
Speaker(s): Nigel Hitchin
Abstract: Critical values of the integrable system correspond to singular spectral curves. In this talk we shall discuss critical points, points in the moduli space where one of the Hamiltonian vector fields vanishes. These involve torsion-free sheaves on the spectral curve instead of line bundles and a lifti... read more
Date: 13/02/2017 - 9:35 am

PIRSA:17020018  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Generalizing Quivers: Bows, Slings, Monowalls
Speaker(s): Sergey Cherkis
Abstract: Quivers emerge naturally in the study of instantons on flat four-space (ADHM), its orbifolds and their deformations, called ALE space (Kronheimer-Nakajima). Pursuing this direction, we study instantons on other hyperkaehler spaces, such as ALF, ALG, and ALH spaces. Each of these cases produces ins... read more
Date: 13/02/2017 - 11:00 am

PIRSA:17020019  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Holomorphic symplectic Morita equivalence and the generalized Kahler potential
Speaker(s): Marco Gualtieri
Abstract: Since the introduction of generalized Kahler geometry in 1984 by Gates, Hull, and Rocek in the context of two-dimensional supersymmetric sigma models, we have lacked a compelling picture of the degrees of freedom inherent in the geometry. In particular, the description of a usual Kahler structure i... read more
Date: 13/02/2017 - 2:00 pm

PIRSA:17020020  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Nahm transformation for parabolic harmonic bundles on the projective line with regular residues
Speaker(s): Szilard Szabo
Abstract: I will define a generalization of the classical Laplace transform for D-modules on the projective line to parabolic harmonic bundles with finitely many logarithmic singularities with regular residues and one irregular singularity, and show some of its properties. The construction involves on the ana... read more
Date: 13/02/2017 - 3:00 pm

PIRSA:17020021  ( MP4 Medium Res , MP3 , PDF ) Which Format?
A mathematical definition of 3d indices
Speaker(s): Tudor Dimofte
Abstract: 3d field theories with N=2 supersymmetry play a special role in the evolving web of connections between geometry and physics originating in the 6d (2,0) theory. Specifically, these 3d theories are associated to 3-manifolds M, and their vacuum structure captures the geometry of local systems on M. (S... read more
Date: 14/02/2017 - 9:30 am

PIRSA:17020022  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Perverse Hirzebruch y-genus of Higgs moduli spaces
Speaker(s): Tamas Hausel
Abstract: I will discuss in the framework of the P=W conjecture, how one can conjecture formulas for the perverse Hirzebruch y-genus of Higgs moduli spaces. The form of the conjecture raises the possibility that they can be obtained as the partition function of a 2D TQFT.
Date: 14/02/2017 - 11:00 am

PIRSA:17020023  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Motivic Classes for Moduli of Connections
Abstract: In their paper, "On the motivic class of the stack of bundles", Behrend and Dhillon were able to derive a formula for the class of a stack of vector bundles on a curve in a completion of the K-ring of varieties. Later, Mozgovoy and Schiffmann performed a similar computation in order to obtain the ... read more
Date: 14/02/2017 - 2:00 pm

PIRSA:17020024  ( MP4 Medium Res , MP3 , PDF ) Which Format?
BPS algebras and twisted character varieties
Speaker(s): Ben Davison
Abstract: In this talk I will explain how a perverse filtration on the Kontsevich-Soibelman cohomological Hall algebra enables us to define the Lie algebra of BPS states associated to a smooth algebra with potential. I will then explain what this means for character varieties, and in particular, how to build... read more
Date: 14/02/2017 - 3:00 pm

PIRSA:17020026  ( MP4 Medium Res , MP3 , PDF ) Which Format?
On index of rigidity
Speaker(s): Kazuki Hiroe
Abstract: The index of rigidity was introduced by Katz as the Euler characteristic of de Rham cohomology of End-connection of a meromorphic connection on curve. As its name suggests, the index valuates the rigidity of the connection on curve. Especially, in P^1 case, this index makes a significant contributio... read more
Date: 15/02/2017 - 9:30 am

PIRSA:17020027  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Symplectic geometry related to G/U and `Sicilian theories'
Speaker(s): Victor Ginzburg
Abstract: We construct an action of the Weyl group on the affine closure of the cotangent bundle on G/U. The construction involves Hamiltonian reduction with respect to the `universal centralizer' and an interesting Lagrangian variety, the Miura variety. A closely related construction produces symplectic mani... read more
Date: 15/02/2017 - 11:00 am

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