Abstract:
The adjoint polynomial of a polytope is the numerator of its canonical form. A mathematically (and, it seems, physically) interesting question is whether adjoints have determinantal representations, that is, can be written as determinants of matrices of linear forms. In this talk I will report on this question. In particular, I will discuss when this is true (and when this is false), present constructive methods to obtain determinantal representations of adjoints and some counterexamples. Our attention will be mostly focused on two- and three-dimensional polytopes as well as on ABHY associahedra. This is joint work in progress with Clemens Brüser and Mario Kummer.
About the speaker:
Dmitrii Pavlov is a postdoctoral researcher in the Real Algebraic Geometry group at TU Dresden. His research focuses on positive geometry using algebraic, combinatorial, and computational tools to better understand the structures underlying physical theories.
The UNIVERSE+ Online Seminar Series is designed to foster dialogue and collaboration among project partners and those interested in positive geometry.
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