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Probabilistic methods in computational complexity and geometry

Grant number: 22/09280-5
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2022
Effective date (End): July 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Theory of Computation
Principal Investigator:Yoshiharu Kohayakawa
Grantee:Théo Borém Fabris
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated scholarship(s):23/13743-3 - Average-case hardness in proof complexity, BE.EP.IC

Abstract

This is an undergraduate research project for Théo Borém Fabris, to be carried out under the supervision of Y. Kohayakawa at the Institute of Mathematics and Statistics of the U. of São Paulo, from 1 October 2022 to 30 September 2023 (12 months). We plan a detailed study, at an undergraduate level, of methods from probability theory to solve problems in mathematics and computer science. This work will involve the study of probabilistic techniques applied to diverse areas, such as combinatorics, number theory, computational complexity and geometry. We also plan the study and implementation of an elementary construction of expander graphs. At the end of this project, which we plan to extend to the end of the student's undergraduate programme, the student will have had a deeper contact with current lines of research in mathematics and computer science, not covered in undergraduate courses, and thus he will be able to start his graduate studies with a strong background.(AU)

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