Topological Recursion for Hurwitz Theory and Intersection Theory of Moduli Spaces of Curves

Explore the intricate connections between topological recursion theory, Hurwitz theory, and the intersection theory of moduli spaces of curves in this comprehensive lecture. Delve into the foundations of topological recursion and its applications to enumerative geometric problems, particularly in Hurwitz theory. Examine the concept of counting branched covers of Riemann surfaces with specific ramification profiles and its significance in defining various Hurwitz enumerative problems. Investigate the relationship between topological recursion-generated numbers and moduli spaces of curves, and analyze the ELSV formula's role in expressing Hurwitz numbers through intersections of Hodge and psi classes. Discover the evolution of ELSV-type formulae and their implications for understanding the link between ramification types and cohomological field theories. Gain insights into current conjectures and the state-of-the-art in this fascinating area of mathematical research.