Abstract:
Invariant theory studies the orbits of the action of a group on a vector space. A key problem in invariant theory is to describe generators of the algebra of all polynomial functions on the vector space that remain invariant under the group action. A related problem is to identify a set of separating invariants, that is, a collection of invariants capable of distinguishing those orbits that can be separated by invariants. In this talk, we present our recent results on invariants and separating invariants of the algebra of split-octonions. Finally, we will briefly discuss applications of invariant theory to machine learning.
Bio:
I completed my Ph.D. in 2004 in Russia under the supervision of Prof. Alexandr Zubkov. Following my doctoral studies, I held a postdoctoral position at Bielefeld University in Germany (16 months in total) under the mentorship of Prof. Claus Ringel. I later served as a Principal Investigator in Prof. Ringel's research group at Bielefeld for one year, and as a Visiting Professor at the Technical University of Munich (15 months in total, across three visits). Over the course of my postdoctoral, research, and visiting appointments, I spent approximately 4.5 years at academic institutions in Germany, Italy, Belgium, and Portugal. At the same time, I held positions as Researcher and later Principal Researcher at the Sobolev Institute of Mathematics in Russia.
Since 2013, I have been at the State University of Campinas, first as a Visiting Professor and later as an Assistant Professor. I have supervised four Ph.D. students who successfully defended their dissertations at the State University of Campinas. In 2023, I was promoted to Associate Professor.
