**Avner
Ash**

**Professor
of Mathematics**

**Boston
College**

**Office**:
550 Maloney

**Phone**:
please use e-mail instead

**E-mail**:
ashav@bc.edu

**Office
hours**: As posted on my office door or by appointment via e-mail

**Books**

*
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) **

**Selected
publications and preprints**

**
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*