Math Department Faculty
Avner Ash
Professor
Avner Ash
Ph.D.
Contact
Maloney Hall 550
Telephone: 617-552-6006
Email: ashav@bc.edu
Education
- Ph.D. Harvard University
Office Hours
As posted on my office door or by appointment via e-mail
Department
Selected publications and preprints
- 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 Gl2(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 Gl3(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 Gl3(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 Gln(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 GL4(Z). III (joint with Paul Gunnells and Mark McConnell) Math. Comp. 79 (2010) 1811-1831
- Cohomology of congruence subgroups of GL4(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 GL3(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
A6-extensions of Q and the mod p cohomology of GL3(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
- SL3(F2)-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 SL4(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,Fp), 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