# Browse Prizes and Awards

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Frank Nelson Cole Prize in Algebra 2024 Jessica Fintzen

The 2024 Frank Nelson Cole Prize in Algebra is awarded to Jessica Fintzen (University of Bonn) for her work transforming the understanding of representations of *p*-adic groups, in particular for the article "Types for tame p-adic groups," *Ann. of Math.* (2) 193 (2021), no. 1, 303–346.

Prize announcement as seen in the news release.

Frank Nelson Cole Prize in Algebra 2021 Chenyang Xu

The 2021 Frank Nelson Cole Prize in Algebra is awarded to Chenyang Xu. He leads 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.

Prize announcement as seen in the news release.

Frank Nelson Cole Prize in Algebra 2018 Robert M Guralnick

Twentieth award: The 2018 Frank Nelson Cole Prize in Algebra was awarded to Robert Guralnick 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.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2015 Peter Scholze

Nineteenth award: The 2015 Frank Nelson Cole Prize in Algebra was awarded to Peter Scholze for his work on perfectoid spaces which has led to a solution of an important special case of the weight-monodromy conjecture of Deligne.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2012 Alexander S. Merkurjev

Eighteenth award: The 2012 Frank Nelson Cole Prize in Algebra was awarded to Alexander S. Merkurjev for his work on the essential dimension of groups.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2009 Christopher Hacon; James McKernan

Seventeenth award: The 2009 Frank Nelson Cole Prize in Algebra was awarded to Christopher Hacon and James McKernan for their groundbreaking joint work on higher dimensional birational algebraic geometry.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2006 János Kollár

Sixteenth award: The 2006 Frank Nelson Cole Prize in Algebra was awarded to János Kollár for his outstanding achievements in the theory of rationally connected varieties and for his illuminating work on a conjecture of Nash.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2003 Hiraku Nakajima

Fifteenth award: The 2003 Frank Nelson Cole Prize in Algebra was awarded to Hiraku Nakajima for his work in representation theory and geometry.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 2000 Andrei Suslin; Aise Johan de Jong

Fourteenth award: The 2000 Frank Nelson Cole Prize in Algebra was awarded to Andrei Suslin for his work on motivic cohomology, and to Aise Johan de Jong for his important work on the resolution of singularities by generically finite maps.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 1995 Michel Raynaud; David Harbater

Thirteenth award: The 1995 Frank Nelson Cole Prize in Algebra was awarded to Michel Raynaud and David Harbater for their solution of Abhyankar's conjecture. This work appeared in the papers Revêtements de la droite affine en caractéristique p > 0, Invent. Math. 116 (1994) 425-462 (Raynaud), and Abhyankar's conjecture on Galois groups over curves, Invent. Math. 117 (1994) 1-25 (Harbater).

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Algebra 1990 Shigefumi Mori

Twelfth award: The 1990 Frank Nelson Cole Prize in Algebra was awarded to Shigefumi Mori for his outstanding work on the classification of algebraic varieties and, in particular, for his paper Flip theorem and the existence of minimal models for 3-folds, Journal of the American Mathematical Society, volume 1 (1988), pp. 117-253.

Frank Nelson Cole Prize in Algebra 1985 George Lusztig

Eleventh award: The 1985 Frank Nelson Cole Prize in Algebra was awarded to George Lusztig for his fundamental work on the representation theory of finite groups of Lie type. In particular for his contributions to the classification of the irreducible representations in characteristic zero of the groups of rational points of reductive groups over finite fields, appearing in Characters of reductive groups over finite fields, Annals of Mathematics Studies, volume 107, Princeton University Press, 1984.

Frank Nelson Cole Prize in Algebra 1980 Michael Aschbacher; Melvin Hochster

Tenth award: The 1980 Frank Nelson Cole Prize in Algebra was awarded to Michael Aschbacher for his paper, A characterization of Chevalley groups over fields of odd order, Annals of Mathematics, Series 2, volume 106 (1977), pp. 353-398; and to Melvin Hochster for his paper Topics in the homological theory of commutative rings, CBMS Regional Conference Series in Mathematics, Number 24, American Mathematical Society, 1975.

Frank Nelson Cole Prize in Algebra 1975 Hyman Bass; Daniel G. Quillen

Ninth award: The 1975 Frank Nelson Cole Prize in Algebra was awarded to Hyman Bass for his paper, Unitary algebraic K-theory, Springer Lecture Notes in Mathematics, volume 343, 1973; and to Daniel G. Quillen for his paper, Higher algebraic K-theories, Springer Lecture Notes in Mathematics, volume 341, 1973.

Frank Nelson Cole Prize in Algebra 1970 John R. Stallings; Richard G. Swan

Eighth award: The 1970 Frank Nelson Cole Prize in Algebra was awarded to John R. Stallings for his paper, On torsion-free groups with infinitely many ends, Annals of Mathematics, Series 2, volume 88 (1968), pp. 312-334; and to Richard G. Swan for his paper, Groups of cohomological dimension one, Journal of Algebra, volume 12 (1969), pp. 585-610.

Frank Nelson Cole Prize in Algebra 1965 Walter Feit; John G. Thompson

Seventh award: The 1965 Frank Nelson Cole Prize in Algebra was awarded to Walter Feit and John G. Thompson for their joint paper, Solvability of groups of odd order, Pacific Journal of Mathematics, volume 13 (1963), pp. 775-1029.

Frank Nelson Cole Prize in Algebra 1960 Serge Lang; Maxwell A. Rosenlicht

Sixth award: The 1960 Frank Nelson Cole Prize in Algebra was awarded to Serge Lang for his paper, Unramified class field theory over function fields in several variables, Annals of Mathematics, Series 2, volume 64 (1956), pp. 285-325; and to Maxwell A. Rosenlicht for his papers, Generalized Jacobian varieties, Annals of Mathematics, Series 2, volume 59 (1954), pp. 505-530, and A universal mapping property of generalized Jacobians, Annals of Mathematics, Series 2, volume 66 (1957), pp. 80-88.

Frank Nelson Cole Prize in Algebra 1954 Harish-Chandra

Fifth award: The 1954 Frank Nelson Cole Prize in Algebra was awarded toHarish-Chandra for his papers on representations of semisimple Lie algebras and groups, and particularly for his paper, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Transactions of the American Mathematical Society, volume 70 (1951), pp. 28-96.

Frank Nelson Cole Prize in Algebra 1949 Richard Brauer

Fourth award: The 1949 Frank Nelson Cole Prize in Algebra was awarded to Richard Brauer for his paper, On Artin's L-series with general group characters, Annals of Mathematics, Series 2, volume 48 (1947), pp. 502-514.

Frank Nelson Cole Prize in Algebra 1944 Oscar Zariski

Third award: The 1944 Frank Nelson Cole Prize in Algebra was awarded to Oscar Zariski for four papers on algebraic varieties published in the American Journal of Mathematics, volumes 61 (1939) and 62 (1940), and in the Annals of Mathematics, Series 2, volumes 40 (1939) and 41 (1940).

Frank Nelson Cole Prize in Algebra 1939 A. Adrian Albert

Second award: The 1939 Frank Nelson Cole Prize in Algebra was awarded to A. Adrian Albert for his papers on the construction of Riemann matrices published in the Annals of Mathematics, Series 2, volume 35 (1934) and volume 36 (1935)

Frank Nelson Cole Prize in Algebra 1928 L. E. Dickson

First award: The 1928 Frank Nelson Cole Prize in Algebra was awarded to L. E. Dickson for his book Algebren und ihre Zahlentheorie, Orell Füssli, Zürich and Leipzig, 1927.