Combinatória em variedades de Schubert

Author(s)

Jordan Lambert Silva

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2017-09-26

Examining board members

Luiz Antonio Barrera San Martin; Viviana Jorgelina Del Barco; David E Anderson; Lucas Conque Seco Ferreira; Laercio Jose dos Santos

• Advisor: Luiz Antonio Barrera San Martin; Lonardo Rabelo

Abstract

This thesis presents combinatorial aspects related to topology/geometry of Schubert varieties. The first problem consists to obtain an explicit formula to compute the coefficients of the boundary operator of the integral homology of real isotropic and odd orthogonal Grassmannians. Despite the geometric nature of this problem, this computation only depends on the combinatorics of permutations associated to Schubert varieties of a cellular decomposition of an isotropic Grassmannians. We also consider a combinatorial study of permutations that are associated to an even more general class of Schubert varieties called theta-vexillary signed permutations. The main result is the development of equivalent descriptions of theta-vexillary permutations in terms of pattern avoidance, and the set of corners of the permutation's diagram (AU)

• FAPESP's process: 13/10467-3 - Geometry of Homogenous space of Loop Groups
• Grantee: Jordan Lambert Silva
• Support Opportunities: Scholarships in Brazil - Doctorate