Organising Committee
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Chiara Damiolini, University of Pennsylvania
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Johan Martens, University of Edinburgh
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Swarnava Mukhopdadhyay, Tata Institute for Fundamental Research
Scientific Advisory Committee
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Iain Gordon, University of Edinburgh
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Jochen Heinloth, Universität Duisburg-Essen
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Frances Kirwan, University of Oxford
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Shrawan Kumar, University of North Carolina at Chapel Hill
About:
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.
Resources
Speakers
| 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 |
