Derived categories and applications to mirror symmetry

• Grant number: 12/21500-9
• Support Opportunities: Scholarships abroad - Research
• Start date: April 22, 2013
• End date: April 21, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Lino Anderson da Silva Grama
• Grantee: Lino Anderson da Silva Grama
• Host Investigator: Ludmil Katzarkov
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Miami, United States

Abstract

This project deals with the study of certain geometric invariants of derived categories that appear in symplectic geometry, namely in Fukaya--Seidel categories. Our first goal is to construct examples of Fukaya-Seidel categories whose Orlov spectrum contains gaps. The second goal is to study Landau--Ginzburg models with multi-potentials in order to describe the Fukaya-Seidel category of a product variety $X_1\times X_2$. (AU)