Higgs bundles and applications

Author(s)

Leonardo Schultz Araujo

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2020-08-18

Examining board members

Lino Anderson da Silva Grama; Eder de Moraes Correa; Ricardo Miranda Martins

• Advisor: Lino Anderson da Silva Grama

Abstract

This dissertation is focused on introducing the concept of Higgs bundles and its moduli space. Covering most of the background theory, we will present some of the surprising correspondence between Higgs bundles and other well-known objects in mathematics. Studying the rich geometry of the moduli space, we will see how this object emerges in Mirror Symmetry as an excellent source of examples on branes interaction under the Mirror duality. We also introduce the Mirror Symmetry theory and, in particular, we discuss the appearance of coisotropic branes and their relation with the complex multiplication over the product of two elliptic curves. We show that the complex multiplication is not necessary to produce such branes. We conclude by using the Hitchin fibration and the special hyperkähler structure on the moduli space of Higgs bundles to understand the action of the Mirror Symmetry over this particular space (AU)

• FAPESP's process: 17/23192-3 - An essay about Higgs bundle and applications
• Grantee: Leonardo Schultz Araujo
• Support Opportunities: Scholarships in Brazil - Master