Publications of Paul Gunnells

More recent publications are in PDF; older publications are in PostScript. Unfortunately this is not up-to-date. My CV has the most current information. You can also find (most of) these on the arXiv.

Appeared/To Appear

• Generalized Catalan numbers from hypergraphs, To appear in Electronic Journal of Combinatorics.
• Hypergraph matrix models, with Mario DeFranco. To appear in Moscow Math Journal.
• On the cohomology of congruence subgroups of GL3 over the Eisenstein integers, with Mark McConnell and Dan Yasaki. To appear in Experimental Math.
• Ironwood meta key agreement and authentication protocol, with Iris Anshel, Derek Atkins, and Dorian Goldfeld. Advances in Mathematics of Communications 15 (2021), no. 3, 397–413.
• Weighted lattice point sums in lattice polytopes, unifying Dehn–Sommerville and Ehrhart–Macdonald, with Matthias Beck and Evgeny Materov. Discrete Comput. Geom. 65 (2021), no. 2, 365–384.
• Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL4(Z) and Galois representations, with Avner Ash and Mark McConnell. J. Algebra 553 (2020), 211–247.
• On the growth of torsion in the cohomology of arithmetic groups, with Avner Ash, Mark McConnell, and Dan Yasaki. J. Inst. Math. Jussieu 19 (2020), no. 2, 537–569.
• On topological computation of K4 of the Gaussian and Eisenstein integers, with Herbert Gangl, Jon Hanke, Achill Schürmann, Matieu Dutour Sirikic, and Dan Yasaki. J. Homotopy Relat. Struct. 14 (2019), no. 1, 281–291.
• Tiered trees, weights, and q-Eulerian numbers, with William Dugan, Sam Glennon, and Einar Steingrímsson. J. Combin. Theory Ser. A 164 (2019), 24–49.
• Exotic matrix models: the Albert algebra and the spin factor. Mosc. Math. J. 18 (2018), no. 2, 321–347.
• Torus orbits on homogeneous varieties and Kac polynomials of quivers, with Emmanuel Letellier and Fernando Rodriguez Villegas. Math. Z. 290 (2018), no. 1–2, 445–467.
• Metaplectic Demazure operators and Whittaker functions, with Gautam Chinta and Anna Puskas. Indiana Univ. Math. J. 66 (2017), no. 3, 1045–1064.
• A class of hash functions based on the algebraic eraser, with Iris Anshel, Derek Atkins, and Dorian Goldfeld. Groups Complex. Cryptol. 8 (2016), no. 1, 1–7.
• On the cohomology of linear groups over imaginary quadratic fields, with Herbert Gangl, Jon Hanke, Achill Schürmann, Matieu Dutour Sirikic, and Dan Yasaki. J. Pure Appl. Algebra 220 (2016), no. 7, 2564–2589.
• A table of elliptic curves over the cubic field of discriminant -23, with Steve Donnelly, Ariah Klages-Mundt, and Dan Yasaki. Exp. Math. 24 (2015), no. 4, 375–390.
• Crystal graphs, Tokuyama’s theorem, and the Gindikin-Karpelevic formula for G_2, with Louis Gaudet and Holley Friedlander. Journal of Algebraic Combinatorics 41 (2015), no. 4, 1089–1102.
• Kazhdan–Lusztig cells in planar hyperbolic Coxeter groups and automata, with Mikhail Belolipetsky and Richard Scott. International Journal of Algebra and Computation 24 (2014), no. 5, 757–772.
• Mod 2 homology of GL(4) and Galois representations, with Avner Ash and Mark McConnell. J. Number Theory 146 (2015), 4–22 (special issue dedicated to Steve Rallis).
• Cells in Coxeter Groups I, with Misha Belolipetsky. J. Algebra 385 (2013), 134–144.
• Lectures on computing cohomology of arithmetic groups, Proceedings of the Conference on Modular Forms, Heidelberg, Germany, 2011. Contributions in Mathematical and Computational Sciences (Springer-Verlag) 6 (2014), 3–45.
• On Hilbert modular threefolds of discriminant 49, with Lev A. Borisov. Selecta Math. (N.S.) 19 (2013), no. 4, 923–947.
• Modular forms and elliptic curves over the cubic field of discriminant −23, with Dan Yasaki. Int. J. Number Theory 9 (2013), no. 1, 53–76.
• Generalized Burnside rings and module categories, with Andrew Rose and D. Rumynin. J. Algebra 358 (2012), 33–50.
• Resolutions of the Steinberg module for GL(n), with Avner Ash and Mark McConnell. J. Algebra 349 (2012), 380–390.
• Metaplectic Ice, with Ben Brubaker, Dan Bump, Gautam Chinta, and Solomon Friedberg, Multiple Dirichlet Series, L-functions and Automorphic Forms, 65–92, Birkhaeuser Boston, 2012.
• Metaplectic Whittaker functions and Crystals of type B, with Ben Brubaker, Dan Bump, and Gautam Chinta, Multiple Dirichlet Series, L-functions and Automorphic Forms, 93–118, Birkhaeuser Boston, 2012.
• Modular forms and elliptic curves over the field of fifth roots of unity, with Farshid Hajir and Dan Yasaki. Experimental Math. 22 (2013), no. 2, 203–216.
• Littelmann patterns and Weyl group multiple Dirichlet series of type D, with Gautam Chinta, Multiple Dirichlet Series, L-functions and Automorphic Forms, 119–130, Birkhaeuser Boston, 2012.
• Kazhdan–Lusztig cells in infinite Coxeter groups, with Misha Belolipetsky. Proceedings of Belfast (UK) meeting Workshop on Algebra, Combinatorics and Dynamics, August 17–21, 2009. J. Gen. Lie Theory Appl. 9 (2015), no. S1, Art. ID S1–002, 4 pp.
• Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations, with Avner Ash and Mark McConnell. J. Algebra 325 (2011), 404–415.
• Automata and cells in affine Weyl groups, Represent. Theory 14 (2010), 627–644.
• On the cohomology of congruence subgroups of SL(4,Z), Proceedings of the RIMS workshop Automorphic representations, automorphic L-functions, and arithmetic, (ed. Yoshi-Hiro Ishikawa), RIMS Kokyuroku 2009.
• Weyl group multiple Dirichlet series of type A2, with Gautam Chinta. Number Theory, Analysis and Geometry: In Memory of Serge Lang, 125–142, Springer, New York, 2012.
• Cohomology of congruence subgroups of SL4 (Z) III, with Avner Ash and Mark McConnell, Math. Comp. 79 (2010), 1811–1831.
• Constructing Weyl group multiple Dirichlet series, with Gautam Chinta, J. Amer. Math. Soc. 23 (2010), 189–215.
• Hecke operators and Hilbert modular forms, with Dan Yasaki, Algorithmic number theory (Banff, 2008), 387–401, Lecture Notes in Comput. Sci., 5011, Springer, Berlin, 2008.
• Cohomology of congruence subgroups of SL(4, Z) II, with Avner Ash and Mark McConnell, J. of Number Theory 128 (2008), no. 8, 2263–2274.
• On the p-parts of quadratic Weyl multiple Dirichlet series, with Gautam Chinta and Solomon Friedberg, J. Reine Angew. Math. 623 (2008), 1–23. J. Reine Angew. Math.
• Lattice polytopes, Hecke operators, and the Ehrhart polynomial, with Fernando Rodriguez Villegas, Selecta Math. 13 (2007), 253–276.
• On certain integral Schreier graphs of the symmetric group, with Richard Scott and Byron Walden, Electronic J. of Combinatorics 14 (2007), no. 1.
• Weyl group multiple Dirichlet series constructed from quadratic twists, with Gautam Chinta, Invent. Math. 167 (2007), no.2, 327–353.
• Robert MacPherson and arithmetic groups, Pure and Appl. Math. Quarterly 2 (2006), no. 4, 1015–1052. Special volume dedicated to Robert MacPherson.
• Computing in higher rank, appendix to the book Modular Forms, a computational approach, by William Stein, GSM v.79, American Math. Society.
• Cells in Coxeter groups, Notices of the AMS, 53 (2006), no. 5, 528–535.
• Geometry of the tetrahedron space, with Eric Babson and Richard Scott. Adv. Math. 204 (2006), no. 1, 176–203.
• Some elementary Ramanujan graphs, Geom. Dedicata. 112 (2005), no. 1, 53–65.
• A characterization of Dynkin elements, with Eric Sommers, Math. Res. Lett. 10 (2003), no. 2–3, 363–373.
• Toric modular forms of higher weight, with Lev A. Borisov, J. Reine Angew. Math. 560 (2003), 43–64.
• Hecke operators and Q-groups associated to self-adjoint homogeneous cones, with Mark McConnell, J. Number Theory 100 (2003), no. 1, 46–71.
• Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions, with Robert Sczech. Duke Math. J. 118 (2003), no. 2, 229–260.
• Wonderful blowups associated to group actions, with Lev A. Borisov, Selecta Math. N.S. 8 (2002), no. 3, 373–379.
• Cohomology of congruence subgroups of SL(4, Z), with Avner Ash and Mark McConnell, J. of Number Theory 94 (2002), 181–212.
• A smooth space of tetrahedra, with Eric Babson and Richard Scott, Adv. Math. 165 (2002), no. 2, 285–312.
• Elliptic functions and equations of modular curves, with Lev A. Borisov and Sorin Popescu, Math. Ann. 321 (2001), no. 3, 553–568.
• Toric varieties and modular forms, with Lev A. Borisov, Invent. Math. 144 (2001), no. 2, 297–325.
• Toric modular forms and nonvanishing of L-functions, with Lev A. Borisov. J. Reine Angew. Math. 539 (2001), 149–165.
• Eisenstein series twisted by modular symbols for the group SL(n), with Dorian Goldfeld. Math. Res. Lett. 7 (2000), 1–10.
• Modular symbols and Hecke operators, Algorithmic number theory (Leiden, 2000), 347–358, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.
• Computing special values of partial zeta functions, with Gautam Chinta and Robert Sczech, Algorithmic number theory (Leiden, 2000), 247–256, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.
• Computing Hecke eigenvalues below the cohomological dimension, J. of Experimental Mathematics 9 (2000), no. 3, 351–367.
• Finiteness of minimal modular symbols for SL(n), J. Number Theory 82 (2000), no. 1, 134–139.
• Symplectic modular symbols Duke Math. J. 102 (2000), no. 2, 329–350
• Modular symbols for rank-one Q-groups and Voronoi reduction, J. Number Theory 75 (1999), no. 2, 198–219.

Submitted/Preprints/Unpublished.

• Units, polyhedra, and a conjecture of Satake, with Jacob Sturm.
• On toric varieties and modular forms, MPIM preprint 2001. This is a writeup of a talk given at the Arbeitstagung, Bonn, 2001.
• On the cryptanalysis of the generalized simultaneous conjugacy search problem and the security of the Algebraic Eraser.
• Defeating the Kalka–Teicher–Tsaban linear algebra attack on the Algebraic Eraser, with Dorian Goldfeld.
• Defeating the Ben-Zvi, Blackburn, and Tsaban Attack on the Algebraic Eraser, with Iris Anshel, Derek Atkins, and Dorian Goldfeld.