Publications
• Numbers with a large prime factor II. Analytic number theory, Essays in honour of Klaus Roth, (2009), 1-14.
• Numbers in a given set with (or without) a large prime factor, Ramanujan Journal, 20 (2010), 275-295.
• Sums of two relatively prime k-th powers, Functiones et Approximatio, 42(1) (2010), 67-112.
• Zeros of a quadratic form at squarefree points, J. Number Theory, 130 (2010), 2119-2146.
• Weyl’s theorem in the measure theory of numbers, Dependence in Probability, Analysis and Number Theory, (2010), 51-72.
• The distribution of k-free numbers, Acta Math. Hungar., 126 (2010), 181-197.
• Primitive lattice points in planar domains, Acta Arithmetica, 142 (2010), 267-302.
• Sequences that omit a box modulo 1, Advances in Math., 227 (2011), 1757-1771.
• Asymptotic Values, Prepoles, and Periodic Points (with Jared Whitehead), International Journal of Bifurcation and Chaos, Vol. 20, No. 4 (2010), 1049-1059.
• Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem (with Tiancheng Ouyang, Duokui Yan, Skyler Simmons, and Gareth Roberts), Celestial Mechanics and Dynamical Astronomy, Vol. 108, No. 2 (2010), 147-164.
• Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem (with Tiancheng Ouyang, Duokui Yan, and Skyler Simmons), Celestial Mechanics and Dynamical Astronomy, Vol. 110, No. 3 (2011), pp 271-290.
• A Profinite Group Invariant for Hyperbolic Toral Automorphisms (with Pedro Martins Rodrigues), Discrete and Continuous Dynamical Systems A, Vol. 36 No. 6 (2012) pp. 1965-1976.
•The Katok-Spatzier Conjecture, Generalized Symmetries, and Equilibrium-Free Flows, to appear in Communications on Pure and Applied Analysis.
• Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem (with Scott C. Mancuso and Skyler C. Simmons), Journal of Mathematical Analysis and Applications 392 (2012) pp. 136-147.
• The minimum rank problem over the finite field of order 2: minimum rank 3, Linear Algebra and its Applications, 430 (2009), 890-923.
• The Inverse Inertia Problem for Graphs: cut vertices, trees, and a counterexample, Linear Algebra and its Applications, 431 (2009), 1147-1191.
• Minimum Rank of Edge Subdivisions of Graphs, Electronic Journal of Linear Algebra, 18 (2009), 530-563.
• Inertia sets for graphs on six or fewer vertices, Electronic Journal of Linear Algebra, 20 (2010), 53-78.
• Zero forcing parameters and minimum rank problems, Linear Algebra and its Applications, 433 (2010), 401-411.
• Computing inertia sets using atoms, Linear Algebra and its Applications, 12 (2011).
• The inverse eigenvalue and inertia problems for minimum rank two graphs, The Electronic Journal of Linear Algebra, 22 (2011), 389-418.
• The inertia set of the join of graphs, Linear Algebra and Its Applications, 434(10) (2011), 11.
• Computing inertia sets using atoms, Linear Algebra Appl. 436(12), 2012, pp. 4489-4502.
• On the graph complement conjecture for minimum rank, Linear Algebra Appl.. 436(12), 2012, pp. 4373-4391.
• Bitwist 3-manifold, Algebraic and Geometric Topology, 9 (2009), 187-220.
• Subdivision rules and virtual endomorphisms, Geometriae dedicate, 141 (2009), 181-195.
• Lattes maps and finites subdivision rules, Conformal Geometry and Dynamics, 14 (2010).
• Cannon's Conjecture, McGraw-Hill Yearbook of Science & Technology, (2011), 39-41.
• What is Thompson's Group?, Notices of the AMS. 58(08) (2011), 2-4.
• Embeddings in manifolds, Bull. Amer. Math. Soc., (2011).
• Extended Laguerre inequalities and a criterion for real zeros, Proceedings of the 7th International ISAAC Congress Imperial College London, UK, (2009), 143-149.
• Matrices related to Dirichlet series, Journal of Number Theory, 130(1) (2010), 27-39.
• Nonnegative minors of minor matrices, (2010), 1-16.
• The Jordan canonical form for a class of zero–one matrices, Linear Algebra and its Applications. 435 (2011), 2942-2954.
• Finite Element Simulation of a Class of Non-Newtonian Fluids with Applications to Industrial Fluids and Blood Flow, Discrete Mathematics
• Errors in approximation and modelling for a glaciology problem, Xiangtan University
• The Combinatorial Structure of the Hawaiian Earring group
• Homotopy of Ends and Boundaries of CAT(0) Groups
• Neighborhood Monotonicity, the Extended Zermelo Model, and Symmetric Knockout Tournaments, Discrete Mathematics, 309 (12) (2009), 3998-4010.
• The Rasch model and additive conjoint measurement, Journal of Applied Measurement, 10 (2009), 348-354.
• Resistance and Conductance in Structured Zermelo Tournaments, Advances in Applied Mathematics, 44(1) (2010), 37-52.
• Using a mathematical model of cadherin-based adhesion to understand the function of the actin cytoskeleton, Physical Review E, 79 (2009).
• Current Opinion in Colloid & Interface Science, 15 (2010), 24-31.
• Multiscale Modeling of Cellular Systems in Biology, Current Opinion in Colloid and Interface Science, Current Opinion in Colloid and Interface Science, (2010).
• Differences in the Mechanism for Myofibroblasts and Vascular Smooth Muscle Cell Populated Collagen Lattice Contraction, Journal of Cellular Biochemistry, 111 (2010), 362-369.
• Understanding Streaming in Dictyostelium discoideum: Theory vs. Experiments, Bulletin of Mathematical Biology, (2011).
• Higher order Schwarzian derivatives for convex univalent functions, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., (2009).
• Typically real harmonic functions, Rocky Mountain J. Math., (2010).
• Convolutions of harmonic mappings, Complex Var. Elliptic Equ., (2010).
• Harmonic mappings onto parallel slit domains, Ann. Polon. Math, 101 (2011), 149-162.
• Typically Real Harmonic Functions, Rocky Mountain J. Math. 42(2), 2012, pp. 567-581.
• Convolutions of harmonic convex mappings, Complex Var. Elliptic Equ. 57(5), 2012, pp. 489-503.
Associate Chair
• A procedure to calculate torsion of elliptic curves over Q, Manuscripta Mathematica 95(1998), 463-469.
• S4- and S4 tilde extensions of Q ramified at only one prime, Journal of Number Theory 75(1999), 185-197.
• Three-dimensional Galois representations with conjectural connections to arithmetic cohomology, in Number Theory for the Millenium, A.K. Peters, Boston, 2002, 365-375.
• Galois representations with conjectural connections to arithmetic cohomology (with Avner Ash and David Pollack), Duke Mathematical Journal 112(2002), 521-579.
• Wild ramification in number field extensions of prime degree, Archiv der Mathematik 81 (2003), 646-649.
• Wildly ramified Galois representations and a generalization of a conjecture of Serre, Experimental Mathematics 14:1 (2005), 119-127.
• Even icosahedral Galois representations with prime conductor (with Michael W. Moore), Journal of Number Theory 118:1, (2006), 62-70
• Explicit Frobenius computations supporting a generalization of a conjecture of Serre (with Brian Hansen), JP Journal of Algebra, Number Theory and Applications, 6 (2006), 381-398.
• Supersingular Galois representations and a generalization of a conjecture of Serre, Experimental Mathematics 16:1 (2007), 119-128
• Distinguishing contragredient Galois representations in characteristic two, Rocky Mountain Journal of Mathematics 38:3 (2008), 835-848.
• Local corrections of discriminant bounds and small degree extensions of quadratic base fields (with Sharon Brueggeman), International Journal of Number Theory 4 (2008), 349-361
• Finding Galois representations corresponding to certain Hecke eigenclasses (with Meghan DeWitt), International Journal of Number Theory 5 (2009), 1-11
• LLL Reduction and a Conjecture of Gunnells (with Russell Ricks), Proceedings of the AMS, 138(2) (2010), 409-415.
• p-adic properties of coefficients of weakly holomorphic modular forms (with Paul Jenkins), International Mathematics Research Notices (2010), 3184-3206.
• Two-divisibility of coefficients of certain weakly holomorphic modular forms, The Ramanujan Journal, 28, (2012), 89-111.
• Complete Integrability of the Reduced Maxwell-Block Equations with Permanent Dipole, Pyshica
• Spontaneous Emission in the Near-Resonant Kapitza-Dirac Effect, Applied Physics
• Real-time dissipation of optical pulses in passive dielectrics, Phys. Rev. A., 80 (2009) 817-827.
• A novel reduction of the simple Asian option and lie-group invariant solutions, Int. J. Theoretical and Appl. Finance, 12 (6) (2009).
• Dispersive dielectrics and time reversal: free energies, orthogonal spectra, and parity in dissipative media, Phys. Rev. E, 82 (2010).
• Intersection Theories and Chebyshev polynomials III., Journal of Algebra and its Applications, 8 (2009), 53-81.
• Counting powers of words in monoids, European Journal of Combinatorics, 30 (2009), 1297-1308.
• Fusions of character tables II: p-groups, Communications in Algebra, 27 (2009), 4296 - 4315.
• Subgroups of free groups generated by conjugates of powers of the generators, Journal of Group theory, 12 (2009), 465-485.
• A note on “conjugacy classes outside a normal subgroup”, Communications in Algebra, 37 (2010), 3306-3308.
• Fusions of character tables III: fusions of cyclic groups and a generalisation of a condition of Camina, Israel Math Journal, 178 (2010), 325-348.
Department Chair
• Logarithmic Trace and Orbifold Products, Duke Mathematical Journal, 153(3) (2010), 427-473.
• On Euler's product of Dedekind zeta function, International Journal of Number Theory, 5 (2009), 293-301.
• A transformation of Hankel type on the field of p-adic numbers, JP Journal of Algebra, Number Theory and Applications, 12 (2009), 205-229.
• On the Euler product of some zeta functions, Combinatorial Number Theory, (2009), 77-99.
• A generalization of A. Connes’ trace formula, Journal of Number Theory, 130(2) (2010), 386-430.
• An adelic Hankel summation formula, Journal of Number Theory, 130(3) (2010), 738-766.
• A spectral interpretation for the explicit formula in the theory of prime numbers, Science China Mathematics, 53(3) (2010), 791-812.
• Prolate spheroidal wave functions, Sonine spaces, and the Riemann zeta function, , J. Math. Anal. Appl.. 389(1), 2012, pp. 379-393.
• Random attractors for stochastic reaction-diffusion equations on unbounded domains, Journal of Differential Equations, 246 (2009), 845-869.
• Invariant Manifolds for Random and Stochastic Partial Differential Equations, Advanced Nonlinear Studies, 10 (2010), 23-52.
• Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space, Memoirs of the American Mathematical Society, 206(967), 2010, 111.
• Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion, Journal of Differential Equations, 248(7) (2010), 1637–1667.
• Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion, Discrete and Continuous Dynamical Systems. Series B., 14(2) (2010), 473–493.
• Chaos in differential equations driven by a nonautonomous force, Nonlinearity, 23(11) (2010), 2935–2975.
• A covering system whose smallest modulus is 40, Journal of Number Theory, 129 (2009), 640-666.
• Nilpotent ideals in polynomial and power series rings, Proc. Amer. Math. Soc, 138(5) (2010), 1607-1619.
• Square-free modules with the exchange property, J. Algebra, 323(7) (2010), 1993-2001.
• The minimal prime spectrum of rings with annihilator conditions, J. Pure Appl. Algebra, 213(7) (2010), 1478-1488.
• On a theorem of Camps and Dicks, Advances in Ring Theory, (2010), 83-84.
— See Jessica Purcell's website.
• Symmetric links and Conway sums: volume and Jones polynomial, Mathematical Research Letters, 16 (2009), 233-253.
• The length of unknotting tunnels, Algebraic and Geometric Topology, 10(2) (2010), 637-661.
• On diagrammatic bounds of knot volumes and spectral invariants, Geometriae Dedicata, 147(1) (2010), 115-130.
• Hyperbolic geometry of multiply twisted knots, Communications in Analysis and Geometry, 18(1) (2010), 101-120.
• On multiply twisted knots that are Seifert fibered or toroidal, Communications in Analysis and Geometry, 18(2) (2010), 219-256.
• Cusp areas of Farey manifolds and applications to knot theory, International Mathematics Research Notices, 23 (2010), 4434-4497.
• Geometric limits of knot complements, Journal of Topology, 3(4) (2010), 759–785.
• An introduction to fully augmented links, Contemporary Mathematics, 541 (2011), 205-220.
• Slopes and colored Jones polynomials of adequate knots, Proceedings of the American Mathematical Society, 139(5) (2011), 1889-1896.
Associate Chair
• Wave motion in a conducting fluid with a boundary layer, Mathematical Analysis
• Waves in a Perfectly Conducting Fluid Filling a Half-Space, IMA
• Generation of Smooth Grids with Line Control for Scattering from Multiple Obstacles, Mathematics and Computers in Simulation, 79 (2009), 2506-2520.
• Elliptic Grids with Nearly Uniform Cell Area and Line Spacing, Electronic Transactions on Numerical Analysis, 34 (2009), 59-75.
• Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering, Journal of Computational Physics, 229 (2010), 5498-5517.
• Finite Difference on Grids with Nearly Uniform Cell Area and Line Spacing for the Wave Equation on Complex Domains, Journal of Computational and Applied Mathematics, 234(6) (2010), 1970-1979.
• Distinguishing Bing-Whitehead Cantor Sets,(with D. Garity, D. Repovs, M. Zeljko) Trans. Amer. Math. Soc. 363 (2011), no. 2, 1007-1022.
