SelectedWorks - Paul Gunnells

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Selected Works of Paul Gunnells

Professor, Department of Mathematics and Statistics

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About Paul Gunnells

Present	Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst
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Algebraic Geometry

Number Theory, Algebraic Geometry, and Topology of Singular Spaces

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Rm 1115L Lederle Grad Research Tower
710 North Pleasant Street
University of Massachusetts Amherst
Amherst MA, 01003
Tel: 413-545-6009
Fax: 413-545-1801

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Articles (18)

Automata and cells in affine Weyl groups

Representation Theory (2010)

Let be an affine Weyl group, and let be a left, right, or two-sided Kazhdan-Lusztig cell in . Let be ...

COHOMOLOGY OF CONGRUENCE SUBGROUPS OF SL4(Z). III

MATHEMATICS OF COMPUTATION (2010)

A Ash, PE Gunnells and M McConnell

In two previous papers we computed cohomology groups for a range of levels , where is the congruence subgroup of ...

CONSTRUCTING WEYL GROUP MULTIPLE DIRICHLET SERIES

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY (2010)

G Chinta and PE Gunnells

Let be a reduced root system of rank . A Weyl group multiple Dirichlet series for is a Dirichlet series ...

Cohomology of congruence subgroups of SL(4, Z) II

JOURNAL OF NUMBER THEORY (2008)

A Ash, PE Gunnells and M McConnell

In a previous paper [3] we computed cohomology groups H5(..0(N),C), where ..0(N) is a certain congruence subgroup of SL(4,Z), for ...

Hecke operators and Hilbert modular forms

ALGORITHMIC NUMBER THEORY (2008)

PE Gunnells and D Yasaki

Let F be a real quadratic field with ring of integers O and with class number 1. Let Γ be ...

On the p-parts of quadratic Weyl group multiple Dirichlet series

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK (2008)

G Chinta, S Friedberg and PE Gunnells

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a ...

Lattice polytopes, Hecke operators, and the Ehrhart polynomial

SELECTA MATHEMATICA-NEW SERIES (2007)

PE Gunnells and FR Villegas

Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial ...

Weyl group multiple Dirichlet series constructed from quadratic characters

INVENTIONES MATHEMATICAE (2007)

G Chinta and PE Gunnells

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to ...

On certain integral Schreier graphs of the symmetric group

Electronic Journal of Combinatorics (2007)

PE Gunnells, RA Scott and BL Walden

We compute the spectrum of the Schreier graph of the symmetric group Sn corresponding to the Young subgroup S2×Sn−2 and ...

Geometry of the tetrahedron space

ADVANCES IN MATHEMATICS (2006)

E Babson, PE Gunnells and R Scott

Let X be the space of all labeled tetrahedra in . In [E. Babson, P.E. Gunnells, R. Scott, A smooth ...

Robert MacPherson and arithmetic groups

PURE AND APPLIED MATHEMATICS QUARTERLY (2006)

We survey contributions of Robert MacPherson to the theory of arithmetic groups. There are two main areas we discuss: (i) ...

Some elementary Ramanujan graphs

GEOMETRIAE DEDICATA (2005)

We give elementary constructions of two infinite families of Ramanujan graphs of unbounded degree. The first uses the geometry of ...

A characterization of Dynkin elements

MATHEMATICAL RESEARCH LETTERS (2003)

PE Gunnells and E Sommers

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a ...

Toric modular forms of higher weight

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK (2003)

LA Borisov and PE Gunnells

Evaluation of Dedekind sums, Eisenstein cocycles, and special values of ...

Duke Mathematical Journal (2003)

PE Gunnells and R Sczech

We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we show how ...

Hecke operators and Q-groups associated to self-adjoint homogeneous cones

Journal of Number Theory (2003)

PE Gunnells and M McConnell

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over , and let ΓG be ...

Cohomology of congruence subgroups of SL4(Z)

JOURNAL OF NUMBER THEORY (2002)

A Ash, PE Gunnells and M McConnell

Let N>1 be an integer, and let Γ=Γ0(N)SL4( ) be the subgroup of matrices with bottom row congruent to (0, ...

A smooth space of tetrahedra

Advances in Mathematics (2002)

E Babson, PE Gunnells and R Scott

This is the pre-published version harvested from ArXiv. We construct a smooth symmetric compactification of the space of all labeled ...

Unpublished Paper

Crystal Graphs, Tokuyama's Theorem, And The Gindikin-Karpelevic Formula For ...

Journal of Algebraic Combinatorics (2014)

Holley Friedlander, Louis Gaudet and Paul E. Gunnells

We conjecture a deformation of the Weyl character formula for type G2 in the spirit of Tokuyama’s formula for type ...

Unpublished Paper

Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata

International Journal of Algebra and Computation (2014)

Mikhail V. Belolipetsky, Paul E. Gunnells and Richard A. Scott

Let C be a one- or two-sided Kazhdan–Lusztig cell in a Coxeter group (W, S), and let Red(C) be the ...

Unpublished Paper

Mod 2 Homology For GL(4) And Galois Representations

Journal of Number Theory (2014)

Avner Ash, Paul E. Gunnells and Mark McConnell

We extend the computations in [AGM11] to find the mod 2 homology in degree 1 of a congruence subgroup Γ ...

Unpublished Paper

A Table Of Elliptic Curves Over The Cubic Field Of ...

Steve Donnelly, Paul Gunnells, Ariah Klages-Mundt and Dan Yasaki

Abstract. Let F be the cubic field of discriminant −23 and OF its ring of integers. Let 􀀀 be the ...

Unpublished Paper

Metaplectic Demazure Operators And Whittaker Functions

Gautam Chinta, Paul Gunnells and Anna Pusk´as

Abstract. In [CG10] the first two named authors defined an action of a Weyl group on rational functions and used ...

Unpublished Paper

On The Cohomology Of Linear Groups Over Imaginary Quadratic Fields

Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schurmann, et al.

Let 􀀀 be the group GLN(OD), where OD is the ring of integers in the imaginary quadratic field with discriminant ...

Unpublished Paper

Torus Orbits On Homogeneous Varieties And Kac Polynomials Of Quivers

Paul Gunnells, Emmanuel Letellier and Fernando Rodriguez Villegas

In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides ...