Explore advanced mathematical concepts in this comprehensive mini-school focusing on wall-crossing structures, analyticity, and resurgence theory. Delve into the innovative approach to resurgent series through analytic wall-crossing structures, offering an alternative to traditional alien calculus methods. Examine detailed examples from quantum Chern-Simons theory, WKB expansions, and holomorphic Floer theory through expert lectures by leading mathematicians including Maxim Kontsevich, Yan Soibelman, Philip Boalch, Lotte Hollands, Kohei Iwaki, Marcos Mariño, Jorgen Andersen, Sergei Gukov, and others. Master topics ranging from global Lie theory and wild Riemann surfaces to supersymmetric quantum field theory, topological recursion, Painlevé equations, exact WKB analysis, topological strings, complex Chern-Simons theory, quantum modularity, resurgent Poisson structures, Donaldson-Thomas invariants, and holomorphic curves. Gain insights into the connections between resurgence theory and various areas of mathematical physics, including quantum invariants, modular forms, and deformation theory through this intensive mathematical program organized by the Institut des Hautes Etudes Scientifiques.

Syllabus

Maxim Kontsevich - 1/4 Introduction to Resurgence via Wall-crossing Structures
Maxim Kontsevich - 2/4 Introduction to Resurgence via Wall-crossing Structures
Philip Boalch - First Steps in Global Lie Theory: wild Riemann surfaces, their character (...)
Lotte Hollands - Wall-crossing and Resurgence in Supersymmetric QFT
Yan Soibelman - 1/3 Holomorphic Floer Theory and Resurgence
Yan Soibelman - 2/3 Holomorphic Floer Theory and Resurgence
Kohei Iwaki - Topological Recursion, Painlevé Equation, Exact WKB and Resurgence
Marcos Mariño - The Resurgent Structure of Topological Strings
Maxim Kontsevich - 3/4 Introduction to Resurgence via Wall-crossing Structures
Yan Soibelman - 3/3 Holomorphic Floer Theory and Resurgence
Maxim Kontsevich - 4/4 Introduction to Resurgence via Wall-crossing Structures
Jorgen Andersen - 1/3 Quantum Chern-Simons Theory, both Real and Complex
Sergei Gukov - Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory
William Mistegard - Resurgence, Quantum Modularity and Quantum Invariants
David Sauzin - On resurgent Poisson structures and deformations
Jorgen Andersen - 2/3 Quantum Chern-Simons Theory, both Real and Complex
Jorgen Andersen - 3/3 Quantum Chern-Simons Theory, both Real and Complex
Pierrick Bousseau - DT Invariants and Holomorphic Curves
Veronica Fantini - q-series, Resurgence and Modularity
Campbell Wheeler - Resurgence and quantum modularity