Lattice polytopes and representation theory (A24)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

We will investigate the combinatorial and metric properties of various types of lattice polytopes. Our motivation stems from open questions in algebraic geometry and representation theory. For example, we investigate moduli spaces of toric degenerations of spherical varieties, induced by birational sequences and monomial bases of their coordinate rings. One goal we pursue is the description of Kostka numbers through lattice polytopes. Furthermore, we aim to make Newton-Okounkov bodies and their alternatives accessible through OSCAR.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Heads: Dr. Xin Fang, since 1/2025; Professor Dr. Ghislain Fourier, since 1/2021; Professor Dr. Michael Joswig, since 1/2021