2020 Topological Recursion Summer School & Workshop
Dates: Sept 7th - 18th, 2020.
Location: Otranto, Italy
A event organized as part ERC Synergy grant ReNewQuantum
Topological recursion (TR) is a tool which first appeared in the context of solving random matrix models. Today it has far reaching applications in algebraic geometry, topological string theory, integrable systems, WKB asymptotic analysis and knots invariants, to name only a few.
In the resolution of matrix integrals, the data is expressed in terms of a spectral curve; an algebraic plane curve together with a heat kernel; representing the random spectrum of the matrices. Topological recursion produces a solution from this data, encoded in differential forms, so called TR "invariants'' of the curve. By abstracting this scheme in terms as a spectral curve input/ invariant output, it was realized that spectral curves arising in the context of matrix models are only one of many possible inputs. Thereafter, several geometric invariants were identified as the TR invariants of new spectral curves. These includes; Gromow-Witten invariants, hyperbolic volumes, knot polynomials, Hurwitz numbers.
Since its introduction in 2007, the subject has attracted the attention of a continuously growing community, including many young researchers. It has been taught in graduate programs internationally,in the Netherlands, United States, China, Canada. It now appears about time to offer a summer school specially dedicated to the subject, aimed at newcoming students. With the 2020 TR Summer School/Worshop we wish to fulfill that need, with the intention of also bringing the community together to inspire the new generation.
It will consist in three parts:
Part I: Mon Sep 7 - Thu Sep 10. Four days of introductory courses on topological recursion, aimed at graduate students. Each day will consist of 4 hours of lectures in the morning and 2 hours exercise session in the afternoon (except for Thursday, that has a free afternoon). Expected attendance: ~ 20 students + 5-10 speakers and organizers
Part II: Fri Sep 11 - Mon Sep 14. Four days of advanced courses on TR,aimed at graduate students and postdocs.4 hours of lectures in the morning and 2 hours exercise session in the afternoon(except for Sunday, which will have an organized social activity )Expected attendance: ~ 40-50 students+postdocs+researchers
Part III: Tue Sep 15 - Fri Sep 18. Four days of workshop, aimed at senior students and researchers.The first day several open problems are proposed, participants then organize in small groups to attack these problems together in the remaining days.Expected attendance: ~ 30 postdocs+researcher
In colaboration with M. Beccaria, D. Dell'Anna (secretary), B. Konopelchenko, G. Landolfi, L. Martina, R. Vitolo, Dipartimento di Matematica e Fisica "E. De Giorgi", Universita' del Salento.