Prize awarded by the American Mathematical Society
The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory.[1] The prize is named after Frank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.[1][2]
The prizes recognize a notable research work in algebra (given every three years) or number theory (given every three years) that has appeared in the last six years. The work must be published in a recognized, peer-reviewed venue. The first award for algebra was made in 1928 to L. E. Dickson, while the first award for number theory was made in 1931 to H. S. Vandiver.[2]
for his groundbreaking research on representation theory, cohomology, and subgroup structure of finite quasi-simple groups, and the wide-ranging applications of this work to other areas of mathematics.
for leading a group developing an algebraic theory of moduli for K-stable Fano varieties and working out a radically new approach to the singularities of the minimal model program using K-stability.
for his papers "Small gaps between primes" (Ann. of Math., 2015), "Large gaps between primes"(Ann. of Math., 2016), and "Primes with restricted digits" (Inv. Math., 2019).
for their astonishing proof of a landmark, sought-after case of the Langlands Conjectures: namely the symmetric power functoriality for holomorphic modular forms (achieved in their two papers: 1. Symmetric power functoriality for holomorphic modular forms, I. Publ. Math. Inst. Hautes Études Sci. 134 (2021), pp. 1-116 2. Symmetric power functoriality for holomorphic modular forms, II. Publ. Math. Inst. Hautes Études Sci. 134 (2021), pp. 117-152)