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- Avner Ash

Professor

Maloney Hall 550

Telephone: 617-552-6006

Email: avner.ash@bc.edu

- Ph.D., Harvard University

As posted on my office door or by appointment via e-mail

*Fearless Symmetry 2nd ed.***(with Robert Gross) Princeton University Press (2008)***Elliptic Tales***(with Robert Gross) Princeton University Press (2012)***Summing It Up***(with Robert Gross) Princeton University Press (2016)***Smooth Compactifications of Locally Symmetric Varietes 2nd ed.***(with D. Mumford, M. Rapoport and Y. Tai and with the collaboration of P. Scholze) Cambridge University Press (2010)**

*Homological vanishing for the Steinberg representation, by Avner Ash, Andrew Putman and Steven V Sam, Compositio Mathematica 154 (2018) 1111-1130.***Even Galois representations and the cohomology of Gl**_{2}**(Z)***(joint with Darrin Doud) preprint***On the growth of torsion in the cohomology of arithmetic groups**(joint with Paul Gunnells and Mark McConnell) preprint**Towards an explicit eigencurve for GL(3)***(joint with David Pollack) Int. J. of Number Th. to appear June 2017***Relaxation of strict parity for reducible Galois representations attached to the homology of Gl**_{3}**(Z)***(joint with Darrin Doud) Int. J. Number Th. 12 (2016) 361-381***Galois representations attached to tensor products of arithmetic cohomology***(joint with Darrin Doud) J. Alg. 465 (2016) 81-99***Mod 2 homology for GL(4) and Galois representations**(joint with Paul Gunnells and Mark McConnell) J Number Theory 146 (2015) 4-22**Highly reducible Galois representations attached to the homology of GL(n,Z)***(joint with Darrin Doud) Proc AMS 143 (2015) 3801-3813***Reducible Galois representations and the homology of Gl**_{3}**(Z)***(joint with Darrin Doud) IMRN 2014 (2014) 1379-1408***Resolutions of the Steinberg representation for GL(n)***(joint with Paul Gunnells and Mark McConnell) J of Alg 349 (2012) 380-390***Direct sums of characters of mod p characters of Gal(Q-bar/Q) and the homology of Gl**_{n}**(Z)***Comm in Alg 41 (2013) 1751-1775***Hecke operators and the stable homology of GL(n)***Comm in Alg 40 (2012) 1369-1387***A constructive approach to p-adic deformations of arithmetic homology**Acta Arithmetica 149 (2011) 305-319**p-adic deformations of arithmetic cohomology--Draft 2007**(joint with Glenn Stevens)**Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations**(joint with Paul Gunnells and Mark McConnell) J. Alg. 325 (2011) 404-415**Cohomology of congruence subgroups of GL**_{4}**(Z). III****(**joint with Paul Gunnells and Mark McConnell)*Math. Comp.*79 (2010) 1811-1831**Cohomology of congruence subgroups of GL**_{4}**(Z) II****(**joint with Paul Gunnells and Mark McConnell)*Journal of Number Theory*128 (2008) 2263-2274**Frequencies of successive pairs of prime residues (**joint with Laura Beltis, Robert Gross and Warren Sinnott)*Experimental Math. J. 20 (2011) 400-411***Equality of polynomial and field discriminants (**joint with Jos Brakenhoff and Theodore Zarrabi)*Experimental Math. J. 16 (2007) 367-374***Frequencies of successive tuples of Frobenius classes (**joint with Brandon Bate and Robert Gross)*Experimental Math. J. 18 (2009) 55-63***Rigidity of p-adic cohomology classes of congruence subgroups of GL(n,Z) (**joint with David Pollack and Glenn Stevens)*Proc LMS (3) 96 (2008) 367-388***Everywhere unramified automorphic cohomology for GL**_{3}**(Z)****(**joint with David Pollack)*Int. Journal of Number Theory 4 (2008) 663-675***Set-theoretic Hida projectors***Proc. Amer. Math. Soc. 137 (2008) 1235-1237***Hecke L-functions and the distribution of totally positive integers**joint with Solomon Friedberg*Canadian J. Math. 59 (2007) 673-695***A**_{6}**-extensions of Q and the mod p cohomology of GL**_{3}**(Z)****(**joint with David Pollack and Warren Sinnott)*Journal of Number Theory, 115 (2005) no. 1, 176-196***Non-vanishing of alternants***Linear Algebra Applications, 411 (2005) 348-355***SL**_{3}**(F**_{2}**)-extensions of Q and arithmetic cohomology modulo 2****(**joint with David Pollack and Dayna Soares)*Experimental Mathematics, 13 (2004) no. 3, 298-307***Smith theory and Hecke operators***Journal of Algebra, 259 (2003) no. 1, 43-58***Cohomology of congruence subgroups of SL**_{4}**(Z)****(**joint with Paul Gunnells and Mark McConnell)*Journal of Number Theory, 94 (2002) no. 1, 181-212***Galois representations with conjectural connections to arithmetic cohomology (**joint with David Pollack and Darren Doud)*Duke Mathematics Journal, 112 (2002) no. 3, 521-579***An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p cohomology of GL(n,Z) (**joint with Warren Sinnott)*Duke Mathematics Journal, 105 (2000) no. 1, 1-24***Generalized non-abelian reciprocity laws: a context for Wiles' proof (**joint with Robert Gross)*Bull. London Math. Soc., 32 (2000), no. 4, 385-397***Modular representations of GL(3,F**_{p}**), symmetric squares, and mod-p cohomology of GL(3,Z) (**joint with Pham Huu Tiep)*Journal of Algebra, 222 (1999) no. 2, 376-399***Monomial Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(p-1,Z)***Math. Ann. 315 (1999), no. 2, 263-28***Galois representations, Hecke operators, and the mod-p cohomology of GL(3,Z) with twisted coefficients (**joint with Gerald Allison and Eric Conrad)*Experimental Mathematics, 7 (1998), no. 4, 361-390***Cohomology at infinity and the well-rounded retract for general linear groups (**joint with Mark McConnell)*Duke Mathematics Journal 90 (1997) no. 3, 549-576***p-adic deformations of cohomology classes of subgroups of GL(n,Z) (**joint with Glenn Stevens)*Journees Arithmetiques, (Barcelona, 1995) Collect. Math. 48 (1997), no. 1-2, 1-30*

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