The structure of (almost) lattices – algebra, analysis, and arithmetic (A01)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 491392403

Studying theta and zeta functions associated with various integral structures allows us to develop original connections between lattice-theoretic enumeration problems, convex geometry, and the theory of modular forms. Concretely we combine, in a novel way, classical Ehrhart theory of convex polytopes with Hecke series of symplectic p-adic Lie groups. Crystallographic counting problems we tackle using methods from algebraic combinatorics and geometry. Lastly we aim at a comprehensive generalization of classical aspects of the theory of modular forms from lattices to almost lattices.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 358: Integral Structures in Geometry and Representation Theory
• Applicant Institution: Universität Bielefeld
• Project Heads: Professorin Dr. Claudia Alfes-Neumann; Professor Dr. Michael Baake; Professor Dr. Christopher Voll