Daniel S. Halpern-Leistner, assistant professor of mathematics, has received a prestigious CAREER award from the National Science Foundation to research recent developments in the theory of algebraic stacks and derived algebraic geometry to develop a general approach to moduli problems. An article on the Cornell Research website describes these problems and Halpern-Leister’s approach:

“Systems of polynomial equations are useful for describing many phenomena in mathematics, engineering, and the physical sciences. Such a system often has a set of solutions with a complicated and interesting multidimensional shape that varies with changes to the system’s parameters. Recently, the problem of determining how altering the system’s parameters affects the geometric properties of the system’s solutions—called a moduli problem—has become important in high-energy theoretical physics.”