Organizing by:
- Tom Bridgeland (University of Sheffield, UK)
- Samuel Grushevsky (Stony Brook University, USA)
- Andrew Neitzke (Yale University, USA)
- Martin Moeller (Universitaet Frankfurt, Germany)
This program in Mathematics is inspired by a circle of ideas originating in quantum field theory and string theory, particularly the study of the quantum field theories “of class S”. These field theories have been the subject of intense study in the high energy theory community over the last thirteen years. Many of the constructions from physics have now found their natural place in vibrant areas of research in pure mathematics. Physical insights have helped to catalyze the realization that the mathematics of flat surfaces, triangulated categories, cluster algebras, symplectic geometry, and ordinary differential equations have a common Rosetta stone, in the theory of meromorphic quadratic differentials on Riemann surfaces.
This program, partly motivated by physics, is structured around meromorphic quadratic differentials on Riemann surfaces, and their relations with stability conditions and enumerative invariants in geometry. We aim to bring these diverse mathematical communities together to focus on the core constructions of mutual interest, to see if techniques from one field can shed light on questions from another, and to make progress in each of the directions separately.
The focus in Week 1 and 2 will be on the geometry of the spaces parameterising quadratic differentials and stability conditions, and the interactions between them
WEEK 1: May 13 – 17, 2024
Mini-course:
Tuesday 5/14/24: 10:30AM – Seminar Room – 313
Wednesday 5/15/24: 10:30AM – Seminar Room – 313
Thursday 5/16/24: 10:30AM – Seminar Room – 313
Speaker: Anton Zorich (University of Paris 7)
Title: Some basic facts about geometry and dynamics of moduli spaces of quadratic differentials
Friday 5/17/24: 10:30AM – Seminar Room – 313
Speaker: Fabian Haiden (Centre for Quantum Mathematics, Denmark)
Title: Introduction to stability conditions
WEEK 2: May 20 – 24, 2024
Mini-course:
Monday 5/20/24: 10:30AM – Seminar Room – 313
Tuesday 5/21/24: 10:30AM – Seminar Room – 313
Speaker: Fabian Haiden (Centre for Quantum Mathematics, Denmark)
Title: Introduction to stability conditions
Wednesday 5/22/24: 10:30AM – Seminar Room – 313
Thursday 5/23/24: 10:30AM – Seminar Room – 313
Friday 5/24/24: 10:30AM – Seminar Room – 313
Speaker: Tom Bridgeland (University of Sheffield)
Title: Geometric structures on spaces of stability conditions induced by Donaldson-Thomas invariants
WEEK 3: May 27 – 31, 2024
FOCUS: Spectral networks and BPS states
Mini-courses:
Speaker: Pierrick Bousseau (University of Georgia)
Title: Scattering diagrams with a view toward spectral networks
Speaker: Andy Neitzke (Yale University)
Title: Introduction to spectral networks
WEEK 4: June 3 – 7, 2024
Workshop: Moduli of Meromorphic Quadratic Differentials devoted to all these topics
WEEK 5: June 10 – 14, 2024
Focus: Discussions and research talks
WEEK 6: June 17 – 21, 2024
Focus: Discussions, research and future outlook talks.
