Bundles and Conformal Blocks with a Twist

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Bundles and Conformal Blocks with a Twist

 13 - 17 Jun 2022

ICMS, Bayes Centre, Edinburgh


Organising Committee

  • Chiara Damiolini, University of Pennsylvania
  • Johan Martens, University of Edinburgh
  • Swarnava Mukhopdadhyay, Tata Institute for Fundamental Research

Scientific Advisory Committee

  • Iain Gordon, University of Edinburgh
  • Jochen Heinloth, Universität Duisburg-Essen
  • Frances Kirwan, University of Oxford
  • Shrawan Kumar, University of North Carolina at Chapel Hill


In the past decades, the theory of moduli spaces of bundles over algebraic curves has played a central role in various branches of mathematics, with deep ties to very active areas such as topological field theories, the Langlands program, and representation theory of affine Lie algebras.
A crucial ingredient that unifies several refinements of the theory came into focus recently: torsors for parahoric Bruhat-Tits group schemes. This gives a uniform approach to level structures, parabolic bundles, prym varieties, and the structures underlying twisted confomal blocks from conformal field theory. 
The last few years have seen the start of a systematic study of these matters, involving different communities of researchers and areas of interest. This conference was the first activity of its kind focused on this development.


Jørgen Andersen, Centre for Quantum Mathematics, SDU Generalized Hitchin Connections with applications to quantization of Moduli Space of parabolic vector bundles
Thomas Baier , IST Lisbon On Hitchin's connection
Vikram Balaji, Chennai Mathematical Institute, Chennai Degenerations of $G$-torsors and Bruhat-Tits group schemes
Prakash Belkale, University of North Carolina at Chapel Hill Rigid local systems and the multiplicative eigenvalue problem
Philip Boalch, IMJ-PRG Paris Diagrams, fission spaces and global Lie theory
Arzu Boysal, Bogazici University Volumes of moduli spaces of flat bundles over surfaces and the Verlinde formula
Emily Cliff, Université de Sherbrooke Moduli spaces of principal 2-group bundles and a categorification of the Freed--Quinn line bundle
Tanmay Deshpande, Tata Institute for Fundamental Research Crossed modular categories and the Verlinde formula for twisted conformal blocks
Angela Gibney, University of Pennsylvania Vector bundles of VOA conformal blocks on the moduli space of stable pointed curves of genus g
Jochen Heinloth, Universität Duisburg-Essen Introductory Mini-Course on Parahoric Torsors
Jiuzu Hong, University of North Carolina at Chapel Hil Twisted conformal blocks and their dimension
Marina Logares, Universidad Complutense de Madrid Assorted Hitchin integrable systems
Christian Pauly, Université Côte d'Azur The Prym-Hitchin connection
Ana Peon-Nieto, University of Birmingham Geometry of wobbly bundles
Michael Rapoport, Math. Inst. Univ. Bonn, Dept. of Math. U. of Maryland Purity for $\mathcal G$-bundles
Maciej Szczesny, Boston University Conformal blocks for complex surfaces and beyond
Constantin Teleman, University of California, Berkeley Higher Verlinde formula and Mirror symmetry
Olga Trapeznikova, University of Geneva The Verlinde formula and K-theory of the moduli space of parabolic vector bundles.
Katrin Wendland, Trinity College Dublin SU(2) channels the cancellation of K3 BPS states
Richard Wentworth, University of Maryland The Hitchin connection for parabolic G-bundles

Sponsors and Funders:

  • Glasgow
  • Foundation
  • EMS
  • NSF
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