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Frank Calegari is a professor of mathematics at the University of Chicago, recognized for his work in the Langlands program. A central theme in his research is the reciprocity conjecture, which seeks to link geometric objects—such as elliptic curves—with analytic ones, such as automorphic forms. He investigates the relationship between Galois representations and automorphic forms using techniques from homology, commutative algebra, arithmetic geometry, and group theory. More recently, Calegari has also explored questions concerning the irrationality of a class of real numbers known as periods, the most famous example being π. Periods are, by definition, values of definite integrals and appear throughout mathematics in both subtle and profound ways.