2025/2026
Moduli Spaces, Dubrovin-Frobenius Manifolds and Topological Recursion
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
When:
1, 2 module
Open to:
students of all HSE University campuses
Language:
English
Contact hours:
60
Course Syllabus
Abstract
"Cohomological field theories were defined in the mid-90s by Kontsevich and Manin to describe the formal properties of the virtual fundamental class in Gromov-Witten theory. The Givental-Teleman classification of cohomological field theories states that any semisimple CohFT with a unit is uniquely determined by its genus 0, descendent-free part (which corresponds to a semisimple Dubrovin-Frobenius manifold) through the so-called Givental R-matrix.
The Chekhov-Eynard-Orantin topological recursion is a universal recursion that arises in various enumerative problems in combinatorics, algebraic geometry, and mathematical physics.
The course will focus on identifying the Givental-Teleman construction with topological recursion, which, in particular, provides an algebro-geometric interpretation of many enumerative combinatorics problems."