Mathematical Sciences: Toric Geometry, Lattice Points in Polytopes, and Zeta Functions

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Morelli This award funds the research of Professor Robert Morelli into toric varieties and lattice point counting. The work is a combination of ideas from several parts of number theory and combinatorics. The work includes developing general techniques for counting points in convex polytopes. The investigator also intends to explore connections between these problems and problems involving zeta functions and modular forms. This work falls into the general areas of Number Theory and Combinatorics. Number Theory is the study of properties of the whole numbers and is the oldest branch of systematic mathematics. Combinatorics is the study of problems involving the counting of complex collections. The research involves establishing general methods for counting regularly distributed points within regular boundaries. This has important application in many different areas of mathematics and science. Recently both Number Theory and Combinatorics have found applications in theoretical computer science and modern communication. ***