Polyhedral Fan Structures in Toric and Tropical Geometry

• Antragsteller: Professor Dr. Michael Joswig
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2010 bis 2017
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 171126520

Lattice polytopes are objects at a junction between combinatorics and algebraic geometry. The study of their triangulations, coarsest subdivisions, mixed subdivisions, and other decompositions is motivated by the mutual interaction between these fields as well as by applications in number theory, optimization, statistics, mathematical physics, and algorithmic biology. Attacking fundamental open problems in this area requires to combine theoretical insight with algorithmic ingenuity and computer experiments. Specific topics addressed in this proposal include the following: unimodular triangulations of lattice polytopes (in particular, matroid polytopes), the relationship between smoothness and normality of a toric variety, combinatorial and geometric interpretations of h∗-polynomials, and symmetric lattice polytopes. Interaction with other researchers in the Priority Program 1489 provides a unique opportunity which makes it likely to make substantial progress.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• Internationaler Bezug: Frankreich, USA
• Beteiligte Personen: Professor Dr. Stéphane Gaubert; Professor Dr. Joseph Gubeladze; Professor Dr. Benjamin Nill; Professor Bernd Sturmfels, Ph.D.