Exact Asymptotics: From Fluid Dynamics to Quantum Geometry
The first TSVP Thematic Program "Exact Asymptotics: From Fluid Dynamics to Quantum Geometry" was held from August 1 - October 28, 2023. All activities took place at the Okinawa Institute of Science and Technology (OIST). In this news article you can learn more about the program and its aims.
Asymptotic methods and perturbation theory are fundamental tools in applied mathematics. These methods have been employed for centuries and are now widely used in practically every field of physical science, from fluid mechanics and medical imaging to condensed matter physics and string theory. We hope to bring together at least four distinct communities within this wide realm, and encourage interaction between different fields:
Applied mathematics: Building on the work of Dingle and Berry in the late 20th century, applied exponential asymptotics is a mature field. There are many successful applications by a diverse range of practitioners to situations as diverse as: the dendritic growth of crystals; the coupling of multiple length scales in fluid flow; nonlinear mappings and chaotic motion; propeller energy flow and aeroacoustic jet noise.
Painleve equations: The solutions to Painleve equations may be regarded as nonlinear analogues of special functions. Painleve equations are ubiquitous in mathematical physics, serving as a beautiful and surprising bridge between classical and quantum physics: on the one hand, the solutions of Painleve equations are related to partition functions of gauge theores; on the other hand, they appear as self-similar reductions of the Korteweg-DeVries wave equation and its variations.
Quantum field theory and quantum geometry: Recently, exact asymptotic methods have gained a new life in the study of quantum fields and strings where these tools yield exact (nonperturbative) descriptions of quantum phenonena using perturbative data alone (e.g. Feynman diagram expansions). In the past decade, it has been observed that exact WKB analysis - a technique for making analytic sense of the WKB approximation in quantum mechanics - plays a fudamental role in describing protected sectors of certain quantum field theories. Recent work has also shown a connection to the theory of random matrices and topological recursion, among others.
We aim to bring together scientists of diverse backgrounds from around the world and encourage interdisciplinary interaction at the intersection of pure mathematics, applied mathematics, and theoretical physics. We will hold regular seminars and give each visitor the opportunity to present their research in a friendly setting to encourage all participants to understand eachother. Furthermore, we will hold:
Mini courses: These will consist of three to five lectures providing an in-depth introduction to specific sub-topics within the program. The courses will be held towards the beginning of the program and will introduce the key ideas of the different participating communities.
Seminars and colloquia: These events will present the latest progress in exact asymptotics and provide an opportunity for participants to showcase their work and encourage scientific exchange. Every participant will be encouraged to give a talk on their research.