Algebra/Topology seminar

Speaker: Danilo Lewanski

Title: Cohomology of moduli spaces of curves from Mathematical Physics

Abstract: The understanding of the cohomology of the moduli spaces of stable curves and its tautological relations is a long standing problem in Algebraic Geometry. What is surprising is how much motivation this problem inherits from other branches of Mathematics and Physics: String theory, Mirror symmetry, Integrable systems, hyperbolic geometry, enumeration of maps on surfaces and Hurwitz theory, Knot theory, Hitchin systems,… dozens of enumerative problems arising from them have a connection with the intersection theory of moduli spaces of curves. We’ll go through some examples, by exploiting the relatively recent method of Eynard-Orantin Topological Recursion (2007), which provides a universal way to recursively generate solutions of these enumerative problems as intersection numbers.