Resurgent Asymptotics in Physics and Mathematics

Coordinators: Gerald Dunne, Ricardo Schiappa, Mikhail Shifman, and Mithat Unsal

Scientific Advisors: Christopher Howls and Wolfgang Lerche

Asymptotics is one of the most powerful mathematical tools in theoretical physics, and recent mathematical progress in the modern theory of resurgent asymptotic analysis (using trans-series) has recently begun to be applied systematically to many current problems of interest in physics, such as matrix models, string theory, and quantum field theory. Mathematically, much progress has been made in the asymptotics of differential and difference equations, both linear and nonlinear, and physical applications have highlighted the importance of localization, complex integrable systems, infinite dimensional Morse theory, saddle point analysis of path integrals and Picard-Lefschetz theory.

The goal of this program is to bring together experts in these diverse fields of physics and mathematics to exchange new ideas and techniques, and to identify the truly significant problems to be addressed in the near future. Specific focus topics include:

  • Resurgence and non-perturbative physics with applications in gauge theory, sigma models, matrix models, string theory, AdS/CFT, supersymmetry, integrability, and localizable QFT. 
  • Resurgent asymptotics of nonlinear differential and difference equations, exact WKB, and Stokes phases.
  • Picard-Lefschetz theory and novel computational methods for semiclassical analysis, lattice gauge theory, and real-time path integrals.