Welcome to the Algebra Group at Innsbruck University!
Our research focuses on Real Algebra and Geometry, with connections to Convexity, Optimization and Functional Analysis.
Real Algebraic Geometry studies semialgebraic sets over the reals or general real closed fields. In algebraic terms, one studies nonnegative polynomials on such sets, and describes them as (generalized) sums of squares. This approach goes back to Hilbert’s 17th Problem. It helps understanding semialgebraic sets and establishes a close connection to optimization, mostly via semidefinite programming. Convex hulls of semialgebraic sets can also be understood via their nonnegative polynomials, and this helps classifying sets for convex optimization. There are also connections to Functional Analysis, via moment problems and non-commutative polynomial inequalities.
If you want to know more, or have questions concerning these topics, feel free to contact us.