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PIRSA:15050050

Topological Recursion for Higgs Bundles and Cohomological Field Theory

APA

Dumitrescu, O. (2015). Topological Recursion for Higgs Bundles and Cohomological Field Theory. Perimeter Institute for Theoretical Physics. https://pirsa.org/15050050

Olivia Dumitrescu University of California System

Talk numberPIRSA:15050050
Source RepositoryPIRSA
Talk Type Conference

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.