Polyhedral Fan Structures in Toric and Tropical Geometry

• Applicant: Professor Dr. Michael Joswig
• Subject Area: Mathematics
• Term: from 2010 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• International Connection: France, USA
• Participating Persons: Professor Dr. Stéphane Gaubert; Professor Dr. Joseph Gubeladze; Professor Dr. Benjamin Nill; Professor Bernd Sturmfels, Ph.D.