Volume polynomials

• Applicant: Professor Dr. Mateusz Michalek
• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 580118961

Volume polynomials arise in several fundamental areas of mathematics - including the geometry of convex bodies, positive semidefinite (PSD) matrices, nef divisors on algebraic varieties, and nef Kähler forms on compact Kähler manifolds. The interplay among these settings has revealed deep analogies, such as those between the Hodge Index Theorem and the Alexandrov-Fenchel inequalities. In this project, we aim to investigate the structural properties of volume polynomials, with particular emphasis on universal polynomial inequalities among their coefficients.

• DFG Programme: Research Grants