Geometric, Algebraic, and Physical structures around the moduli of Meromorphic Quadratic Differentials: May 13, 2024 – June 21, 2024

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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-courses:

Speaker: Fabian Haiden (Centre for Quantum Mathematics, Denmark)
Title: Introduction to stability conditions

Speaker: Anton Zorich* (University of Paris 7)
Title: Some basic facts about geometry and dynamics of moduli spaces of quadratic differentials

WEEK 2: May 20 – 24, 2024

Mini-course:

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.