Logical and categorical methods in calculus of variations: an Introduction.

• Grant number: 24/16321-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Stefano Nardulli
• Grantee: Mayck Brando Santos Moreira
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated research grant: 21/05256-0 - Geometric variational problems: existence, regularity and geometrical characterization of the solutions, AP.JP

Abstract

The Calculus of Variations is an active area of research with connections and applications in various branches of Mathematics and Mathematical Physics. This project aims to introduce the student to some modern approaches in the calculus of variations, involving tools from Nonstandard Analysis and Topos Theory, preparing them to engage with current research and facilitating their integration into research groups on related topics at public universities in the State of São Paulo. I (Stefano Nardulli) am collaborating on this topic with groups such as Hugo Mariano's at USP and Viviane del Barco's at Unicampi. (AU)