About the project.
Topological recursion is a universal procedure that computes invariants of orientable surfaces (intersection numbers in moduli spaces of curves, Weil–Petersson volumes, Gromov–Witten invariants, enumeration of graphs on surfaces) and relates them to integrability and matrix models.
For non-orientable surfaces and real structures, this theory is still very poorly developed.
A refinement parameter b interpolates between the two worlds: b = 0 corresponds to orientable surfaces (complex structures) and b = 1 to those not necessarily orientable (real structures).
This project, funded by a Leonardo Grant from the
BBVA Foundation (August 2026 – January 2028), is a first step, focused on b = 1, of a longer-term research program.
It addresses three specific problems: the reconstruction of Givental–Teleman in the real case (preferred line for this position);
the volumes of moduli spaces of Klein surfaces, calculated by geometric and recursive means;
and a non-orientable version of the master relation between graphs on ordinary and totally simple surfaces, linked to the orthogonal set of real symmetric matrices.
Activities (2027).
The contracted person will participate, with expenses covered, in the international conference «Mathematical physics and the future of topological recursion» (Humboldt University of Berlin), which commemorates 20 years of topological recursion and which the principal investigator co-organizes.
He will also participate in a workshop at the UPC on the geometric aspects of the project with four international experts.
Duration and environment.
The initial contract is for one year and can be extended for another year with another research grant from the principal investigator.
The position is assigned to the Geometry of Varieties and Applications (GEOMVAP) research group of the Department of Mathematics of the UPC, in Barcelona, and to the
SYMCREA unit of excellence.
The principal investigator, Elba Garcia-Failde (Ramón y Cajal researcher), works on topological recursion, moduli spaces of curves, integrability and free probability.
The working language of the project is English.
Scientific inquiries: .
Mission:Develop research in real and non-orientable enumerative geometry, preferably on cohomological field theories and Gromov–Witten theory in the real case.
Functions to be developed: • Investigate cohomological field theories and their reconstruction in the real case (real Gromov–Witten theory, moduli spaces of real curves).
• Study enumerative invariants of non-orientable surfaces, from the geometric and recursive point of view.
• Develop other lines of the project related to topological recursion, integrability, matrix models or the combinatorics of graphs on surfaces.
• Participate in the scientific activities of the project and the research group, and collaborate with the principal investigator and, possibly, also with international collaborators.
• Write scientific articles with the results and present them at seminars, workshops and international conferences.