Mathematician Boris Bukh Receives NSF CAREER Award
By Jocelyn Duffy
Carnegie Mellon University mathematician Boris Bukh has received a Faculty Early Career Development (CAREER) award from the National Science Foundation. One of the most prestigious awards for young faculty, CAREER awards recognize and support those who exemplify the role of teacher-scholars through their outstanding research and teaching.
Bukh, an assistant professor of mathematical sciences, received the five-year grant to support his research into developing a powerful and novel approach to establish connections between two fundamental mathematical fields: combinatorics and algebra.
Many problems in mathematics and physics involve finding the largest mathematical structure that can result from constraints put on the substructures. These largest structures, called extremal structures, have a remarkable number of applications to other areas of mathematics and science, including theoretical computer science, statistical physics and coding theory.
Under his CAREER grant, Bukh plans to investigate in depth the interplay between extremal structures common to both combinatorics and algebra. There are several problems currently known to be at the interface of these two fields, including explicit constructions of Ramsey graphs, constructions of large graphs not containing a specific subgraph, bounds on spherical codes, zero-error capacities of communication channels and set families with restricted intersections. Bukh is an expert in creating novel algebraic and geometric methods for application to such combinatorial problems.
Bukh will work closely with both undergraduate and graduate students on this research project. He also plans to prepare educational materials for both students and experts that cover the new techniques.