Sebastian Debus

Sebastian Debus is an active Researcher at Technische Universität Chemnitz, regularly contributing to academic discourse through presentations at specialized seminars including the Oberseminar Diskrete Mathematik, Geometrie und Optimierung—a collaborative series between Goethe-Universität Frankfurt and TU Chemnitz. His work bridges theoretical mathematics and computational applications with concrete industry relevance.

His research centers on symmetric function inequalities and superdominance order, specifically analyzing homogeneous symmetric function inequalities across variable counts. He investigates cones of symmetric sums of squares versus nonnegative polynomials, leveraging tropicalization to uncover combinatorial structures. Key contributions include identifying symmetric quartics that are nonnegative but not sums of squares in non-trivial variable counts, with applications in polynomial optimization where set-theoretic differences between these cones are critical. His methodology combines algebraic geometry with discrete combinatorial frameworks to solve foundational problems in optimization theory.

Dr. Debus collaborates internationally, as evidenced by joint work with researchers from diverse institutions including J. Acevedo, G. Blekherman, and C. Riener. His current projects focus on extending tropicalization techniques to higher-degree polynomials and exploring the superdominance order's implications for power-sum inequalities on nonnegative orthants, potentially impacting computational algebra systems and optimization algorithms.