The 2020 School and Workshop in Topological Recursion will take place Sept. 7th - 18th in Otranto, Salento, Italy. This event is organized by the ReNewQuantum ERC Synergy Grant team at IPhT; Bertrand Eynard, Elba Garcia-Falde, Danilo Lewanski & Adrien Ooms. The event will consist in three parts, 4 days each. Each part can be attended independantly. The first two parts will be dedicated to a summer school for graduate students, with an introductory school and advanced school. The third and last part will consist of an open problem workshop, where senior participants will be asked to submit problems to work on in small groups. With this event we hope to bring together the entire spectrum of the topological recursion community. Graduate students who are not familiar with the topic of topological recursion, but who would like to learn about it and use it in their research are welcome to apply to the introductory and advanced school. Senior graduate students in the field and young researchers are invited to participate to the advanced school and workshop.
Topological recursion is an algebra-geometric construction which takes the spectral curve and makes out of it a recursive definition of infinite sequences of symmetric meromorphic n-forms with poles. It was first discovered for random matrices. A main goal of random matrix theory is to find the large size asymptotic expansion of n-point correlation functions, and in some cases, the asymptotic expansion takes the form of an infinite series. The n-form ω(g,n) is than the gth coefficient in the asymptotic expansion of the n-point correlation function. It was found that the coefficients ω(g,n) always obey the same recursion on 2 g -2 +n. The idea is to consider this universal recursion relation beyond random matrix theory, and to promote it as a definition of algebraic curve invariants, was first introduced by Eynard-Orantin in 2007, where they studied the main properties of these invariants.