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Morrissey College of Arts and Sciences

Avner Ash

department of mathematics


Ph.D. Harvard University


Professional History

  • Alfred P. Sloan Foundation Fellowship, 1979-1981

My research is primarily in Number Theory. I study connections between automorphic forms, representations of Galois groups into matrix groups, and the cohomology of arithmetic groups, especially subgroups of the general linear group over rings of integers in number fields. This nexus of theories was involved in the proof of Fermat’s Last Theorem (FLT) by Wiles and Taylor-Wiles. A popular exposition of some of these ideas, and how they are applied to FLT, may be found in the second and third parts of my book with Robert Gross: Fearless Symmetry: Exposing the Hidden Patterns of Numbers, Princeton University Press 2006, new paperback edition 2008.

Selected Publications

  • The Modular Symbol and Continued Fractions in Higher Dimensions, with L. Rudolph, Inv. Math. 55 (1979) 241-250.
  • p-adic L-functions for GL(2n), with D. Ginzburg, Inv. Math. 116 (1994) 27-73.
  • Cohomology of GL(3,Z) and Galois representations, with D. Doud and D. Pollack, Duke Math. J. 112 (2002) 521-579.
  • Rigidity of p-adic cohomology classes of congruence subgroups of GL(n,Z), with D. Pollack and G. Stevens, Proc. London Math. Soc. (3) 96 (2008) 367-388.
  • Cohomology of congruence subgroups of GL(4,Z) II, with P. Gunnells and M. McConnell, J. Number Theory 128 (2008) 2263-2274.