Separating invariants and graph isomorphism problem

• Grant number: 23/17918-2
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2024
• End date: January 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Artem Lopatin
• Grantee: Artem Lopatin
• Host Investigator: Gregor Kemper
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Technical University of Munich (TUM), Germany

Abstract

The subject of the project is algebra, specifically, Invariant Theory. The notion of separating invariants was introduced by Derksen and Kemper in 2002 as a simplification of the notion of invariant generators. A set S of the invariant algebra is called separating if it separates any elements of the space that are separated by some invariant. In many applications of invariants it is sufficient to know only separating invariants. Furthermore, it is well known that in many cases separate invariants have finer properties than generating invariants. From results by Domokos, Draisma, Grosshans, Kemper, Wehlau we know that for any algebra of invariants there is the minimum integer B such that the set of all invariants with a degree less than or equal to B is a separator. In the project we will study separating sets and the number B for invariant algebras of multi-symmetric polynomials and we will consider applications to the graph isomorphism problem and the material elasticity problem.