Hitchin Systems in Mathematics and Physics
Organizer(s):
Collection URL: http://pirsa.org/C17001
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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 torsionfree sheaves on the spectral curve instead of line bundles and a lifti... read more
Date: 13/02/2017  9:35 am
Collection: Hitchin Systems in Mathematics and Physics

Generalizing Quivers: Bows, Slings, Monowalls Speaker(s): Sergey Cherkis
Abstract: Quivers emerge naturally in the study of instantons on flat fourspace (ADHM), its orbifolds and their deformations, called ALE space (KronheimerNakajima). 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
Collection: Hitchin Systems in Mathematics and Physics

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 twodimensional 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
Collection: Hitchin Systems in Mathematics and Physics

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 Dmodules 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
Collection: Hitchin Systems in Mathematics and Physics

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 3manifolds M, and their vacuum structure captures the geometry of local systems on M. (S... read more
Date: 14/02/2017  9:30 am
Collection: Hitchin Systems in Mathematics and Physics

Perverse Hirzebruch ygenus 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 ygenus 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
Collection: Hitchin Systems in Mathematics and Physics

Motivic Classes for Moduli of Connections Speaker(s): Alexander Soibelman
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 Kring of varieties. Later, Mozgovoy and Schiffmann performed a similar computation in order to obtain the ... read more
Date: 14/02/2017  2:00 pm
Collection: Hitchin Systems in Mathematics and Physics

BPS algebras and twisted character varieties Speaker(s): Ben Davison
Abstract: In this talk I will explain how a perverse filtration on the KontsevichSoibelman 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
Collection: Hitchin Systems in Mathematics and Physics

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 Endconnection 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
Collection: Hitchin Systems in Mathematics and Physics

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
Collection: Hitchin Systems in Mathematics and Physics

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