On the Bárány-Larman conjecture, Tverberg's theorem and related topics

• Grant number: 24/14246-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2024
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edivaldo Lopes dos Santos
• Grantee: Leandro Vicente Mauri
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 22/16455-6 - Algebraic, geometric, and differential topology, AP.TEM

Abstract

Algebraic Topology tools have been extremely important in solving problems in Combinatorics and Discrete Geometry, for example there is a very strong relation between Tverberg-type problems and the Borsuk-Ulam Theorem. In this sense, the problems that will be addressed in this research project are:- Study new generalizations based on the Tverberg Topological Conjecture and seek applications of the Tverberg Topological Theorem with other problems in Discrete Geometry and Graph Theory.- Study new generalizations based on the Bárany-Larman colored problem and the colored Tverberg problem by Zivaljevic and Vrecica. - Obtain new results in Van-Kampen-Flores problems, which are directly related to Tverberg's Theorem. More specifically, we intend to obtain results in cases where r is not necessarily a prime power or the set of vertices of the simplex is modified. (AU)