Seminars

BC seminars

BU number theory seminar

Harvard math seminars

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

Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL(4,Z) and Galois representations (with P. Gunnells and M. McConnell), submitted.

Lattice-packing by spheres and eutactic forms (with R. Gross), to appear Experimental Mathematics.

Sums of Galois representations and arithmetic homology (joint with Darrin Doud), to appear TAMS.

Reducible Galois representations and arithmetic homology for GL(4) (joint with Darrin Doud), to appear Annales Mathématiques Blaise Pascal.

Vanishing of the cohomology of the rational points of a reductive Q-group in high dimensions (with A. Putman and S. Sam), Compositio Mathematica. 154 (2018) 1111-1130.

Comparison of Steinberg modules for a field and a subfield, J of Algebra 507 (2018), 200-224.

Even Galois representations and the cohomology of Gl₂(Z) (joint with Darrin Doud) Annales Mathématiques Québec 43 (2019) 1-35.

On the growth of torsion in the cohomology of arithmetic groups(joint with Paul Gunnells, Mark McConnell and Dan Yasaki), Journal of the Mathematical Institute at the University of Paris Jussieu, published online: 21 March 2018, pp. 1-33.

Towards an explicit eigencurve for GL(3) (joint with David Pollack) Int. J. of Number Th. 13 (2017) 1213-1231.

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 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 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,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