Lattice points in moduli spaces of curves

          @misc{ scivideos_PIRSA:10050029,
            doi = {10.48660/10050029},
            url = {https://pirsa.org/10050029},
            author = {Do, Norman},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Lattice points in moduli spaces of curves},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2010},
            month = {may},
            note = {PIRSA:10050029 see, \url{https://scivideos.org/pirsa/10050029}}
          }
          

Abstract

There appear to be only two essentially distinct ways to understand intersection numbers on moduli spaces of curves --- via Hurwitz numbers or symplectic volumes. In this talk, we will consider polynomials defined by Norbury which bridge the gap between these two pictures. They appear in the enumeration of lattice points in moduli spaces of curves and it appears that their coefficients store interesting information. We will also describe a connection between these polynomials and the topological recursion defined by Eynard and Orantin.