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.