K-theory and twisted K-theory

• Grant number: 19/22159-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2020
• End date: February 28, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Gabriel Longatto Clemente
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The candidate intends to deepen his knowledge on K-theory, considering its various significant versions and their main applications. Moreover, he is going to analyse in detail the construction of the most relevant models of twisted K-theory. In particular, he will concentrate on the model through twisted vector bundles, trying to show directly that it represents a twisted cohomology theory. (AU)