Topological Recursion for Higgs Bundles and Cohomological Field Theory

          @misc{ scivideos_PIRSA:15050050,
            doi = {10.48660/15050050},
            url = {https://pirsa.org/15050050},
            author = {Dumitrescu, Olivia},
            keywords = {Mathematical physics},
            language = {en},
            title = {Topological Recursion for Higgs Bundles and Cohomological Field Theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2015},
            month = {may},
            note = {PIRSA:15050050 see, \url{https://scivideos.org/index.php/pirsa/15050050}}
          }
          

Abstract

I will give a brief overview of Topological Recursion and present the general setting and our contribution to this field via geometry and topology techniques. In particular, I will discuss the toplogical recursion applied to the family of spectral curves of Hitchen modulo spaces of Higgs bundles over a smooth base curve C. We study meromorphic Higgs fields of rank two and we realized their spectral curves as divisors in the compactifed cotangent bundle. Topological recursion gives a way to quantize the spectral curve of a Higgs bundle. I will present as typical examples of our theory, some well-known constructions as the recursion of Witten-Kontsevich intersection numbers and the recursion of Catalan numbers, that count the number of cellular graphs on a Riemann Surfaces. In particular, we present a model for the twisted version of the Topological Recursion via Cohomological Field Theory for Mg;n(BG). We prove tat edge contraction axioms of cellular graphs leads to a TQFT.