Research

Faculty Research

Mathematics | Statistics

Mathematics Faculty Research

, Ph.D., SUNY-Albany, 1999; Professor.

Research Interests: Complex analysis, interpolation, extremal problems in Hardy and Bergman spaces.

Selected Publications

  • Jensen-type inequalities and radial null sets (with B. Korenblum), Analysis 21 (2001), 99鈥105. 
  • Some coefficient estimates for \(H^P\) functions (with B. Korenblum), 鈥淐omplex Analysis and Dynamical Systems鈥, Contemporary Mathematics, vol. 364, 2004, pp. 5鈥14. 
  • Remarks on the Bohr phenomenon (with A. Dahlner and D. Khavinson), Computational Methods and Function Theory 4 (2004), no. 1, 1鈥19. 
  • Extremal problems for non-vanishing functions in Bergman spaces (with D. Aharonov, D. Khavinson and H. S. Shapiro), Operator Theory: Advances and Applications 158 (2005), 59鈥86. 
  • The isoperimetric inequality via approximation theory and free boundary problems(with D. Khavinson), Computational Methods and Function Theory 6 (2006), no. 2, 253鈥274.

, Ph.D., Theory, 脡cole Polytechnique 鈥 Paris, 2010; Professor.

Research interests: Study of number fields and lattice ideals; computational algebra.

, Ph.D., University of Pittsburgh, 1999; Professor.

Research interests: Analysis, nonlinear partial differential equations, and potential theory in sub-Riemannian and general metric spaces.

Selected Publications

  • The parbolic infinite-Laplace equation in Carnot groups (with E. Martin), Mich. Math. J. 63 (2016), no. 3, 489鈥509. 
  • Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces (with K. Childers), Proc. Amer. Math. Soc. 142 (2014), no. 3, 989鈥1003. 
  • A sub-Riemannian maximum principle and its application to the pp-Laplacian in Carnot groups, Ann. Acad. Sci. Fenn. 37 (2012), 119鈥134. 
  • The Carnot-Carath茅odory distance vis-a-vis the eikonal equation and the infinite Laplacian, Bull. London Math. Soc. 42 (2010), no. 3, 395鈥404. 
  • The Carnot-Carath茅odory distance and the infinite Laplacian (with F. Dragoni and J. Manfredi), J. Geo. Anal. 19 (2009), no. 4, 737鈥754. 
  • The \(P\)-Laplace equation on a class of Grushin-type spaces (with J. Gong), Proc. Amer. Math. Soc. 134 (2006), no. 12, 3585鈥3594. 
  • On 鈭-harmonic functions on the Heisenberg group, Comm. PDE 27 (2002), nos. 3-4, 727鈥761. 
  • Lipschitz extensions on generalized Grushin spaces, Mich. Math. J. 53 (2005), no. 1, 3鈥31. 
  • The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carath茅odory metrics (with L. Capogna), Trans. Amer. Math. Soc. 357 (2005), no. 2, 795鈥823.

, Ph.D., University of Wisconsin-Madison, 1996; Associate Professor.

Research Interests: The algebraic combinatorics of distance-regular graphs, spin models, Bose-Mesner algebras, and planar algebras.

Selected Publications

  • Distance-regular graphs related to the quantum enveloping algebra of \(\mathrm{sl}(2)\) (with K. Nomura), Journal of Algebraic Combinatorics 12 (2000), 25鈥36. 
  • The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph, Journal of Combinatorial Theory, Series B 81 (2001), 125鈥141. 
  • Spin models and hyper-self-dual Bose-Mesner algebras (with K. Nomura), Journal of Algebraic Combinatorics 13 (2001), 173鈥186. 
  • Some planar algebras related to graphs, Pacific J. Math. 209 (2003), no. 2, 231鈥248.

, Ph.D., Institute of Mathematics of Academy of Sciences of Armenia, 1987; Professor.

Research Interests: Complex analysis and approximation theory.

Selected Publications

  • Rubel's problem on bounded analytic functions, Ann. Acad. Sci. Fenn. Math. 41 (2016), no. 2, 813鈥816. 
  • A theorem of Lohwater and Piranian, Proc. Amer. Math. Soc. 144 (2016), no. 9, 3919鈥3920. 
  • A converse to a theorem of Salem and Zygmund (with V. Totik), Bull. Sci. Math. 140 (2016), no. 3, 260鈥272. 
  • On the zero-free polynomial approximation problem, J. Approx. Theory 205 (2016), 60鈥63. 
  • Weak-star convergence and a polynomial approximation problem, Results Math. 69 (2016), no. 1-2, 257鈥262. 
  • On the peak points, Complex Var. Elliptic Equ. 60 (2015), no. 11, 1475鈥1479. 
  • On a polynomial approximation problem, J. Approx. Theory 162 (2010), no. 4, 717鈥722. 
  • On a problem of M. A. Lavrent'ev on the representability of functions by polynomial series in the complex plane, Izv. Math. 63 (1999), no. 2, 245鈥254.

, Ph.D., University of Nice-Sophia Antipolis (France), 1996; Professor.

Research Interests: Low dimensional topology, quantum algebra, and knot theory.

Selected Publications

  • Ring theoretic aspects of quandles (with N. Fernando and B. Tsvelikhovskiy), J. Algebra 526 (2019), 166鈥187.
  • Quasi-trivial quandles and biquandles, cocycle enhancements and link-homotopy of pretzel links (with M. Liu and S. Nelson), J. Knot Theory Ramifications 27 (2018), no. 11, 1843007, 16 pp.
  • Finitely stable racks and rack representations (with E. Moutuou), Comm. Algebra 46 (2018), no. 11, 4787鈥4802.
  • On the classification of topological quandles (with Z. Chend and B. Shekhtman), Topology Appl. 248 (2018), 64鈥74.
  • On rational knots and links in the solid torus (with K. Bataineh and M. Hajij), Mediterr. J. Math. 15 (2018), no. 4, Art. 171, 20 pp.
  • Twist regions and coefficients stability of the colored Jones polynomial (with M. Hajij and M. Saito), Trans. Amer. Math. Soc. 370 (2018), no. 7, 5155鈥5177.
  • Pretzel knots and \(q\)-series (with M. Hajij), Osaka J. Math. 54 (2017), no. 2, 363鈥381. The colored Jones polynomial of singular knots (with K. Bataineh and M. Hajij), New York J. Math. 22 (2016), 1439鈥1456.
  • Foundations of topological racks and quandles (with E. Moutuou), J. Knot Theory Ramifications 25 (2016), no. 3, 1640002, 17 pp.
  • Quandles鈥攁n introduction to the algebra of knots (with S. Nelson), Student Mathematical Library, 74. American Mathematical Society, 2015. x+245 pp.

, Ph.D., University of Illinois at Chicago, 1990; Professor.

Research Interests: Algebra: finite fields and finite rings, classical groups over finite fields; Number Theory: number theory of finite fields, exponential sums, function fields over finite fields, p-adic fields; Coding Theory and Cryptography: covering radius, Reed-Muller codes, number of inequivalent codes, group actions on Boolean functions; Combinatorics: bent functions, difference sets, applications of finite fields in combinatorics; Topology: knot invariants.

Selected Publications

  • Some results on the covering radii of Reed-Muller codes, IEEE Trans. Inform. Theory 39 (1993), 366鈥378. 
  • \(\mathrm{AGL}(m,2)\) acting on \(R(r,m)/R(s,m)\), J. Algebra 171 (1995), 921鈥938. 
  • Results on bent functions (with P. Langevin), J. Combin. Theory A 80 (1997), 232鈥246. 
  • A generalization of an addition theorem of Kneser (with K. H. Leung and Q. Xiang), J. Number Theory 97 (2002), 1鈥9. 
  • Enumeration of isomorphism classes of extensions of \(p\)-adic fields (with K. Keating), J. Number Theory 104 (2004), 14鈥61.
  • Solution to a problem of S. Payne, Proc. Amer. Math. Soc. 132 (2004), 1鈥8. 
  • A note on the proof of a theorem of Katz, Finite Fields Appl. 11 (2005), 316鈥319. 
  • Reversed Dickson permutation polynomials over finite fields (with G. L. Mullen, J. A. Sellers and J. L. Yucas), Finite Fields Appl. 15(2009), 748鈥773. 
  • Automorphism groups of Alexander quandles, J. Algebra 344 (2011), 373鈥385. 
  • Connected quandles associated with pointed abelian groups (with W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman), Pacific J. Math. 264 (2013), 31鈥60. 
  • A new approach to permutation polynomials over finite fields, II (with N. Fernando and S. D. Lappano), Finite Fields Appl. 22 (2013), 122鈥158. 
  • Permutation polynomials over finite fields鈥攁 survey of recent advances, Finite Fields Appl. 32 (2015), 82鈥119. 
  • Switchings of semifield multiplications (with F. Ozbudak and Y. Zhou), Des. Codes Cryptogr. 80 (2016), 217鈥239. 
  • On global \(\mathcal{P}\)-forms, J. Number Theory 160 (2016), 307鈥325. 
  • Polynomials meeting Ax's bound, Acta Arith. 176 (2016), 65鈥80. 
  • Proof of a conjecture on monomial graphs (with S. D. Lappano and F. Lazebnik), Finite Fields Appl. 43 (2017), 42鈥68.

, Ph.D., SUNY-Binghamton, 1993; Distinguished University Professor.

Research Interests: Interaction between formal language theory and symbolic dynamics, cellular automata and picture languages, computation with splicing languages and connections to splicing DNA. In particular, I am interested in algorithms and mathematical problems rising from DNA-based computations.

Selected Publications

  • Three Dimensional DNA Structures in Computing, BioSystems 52 (1999), 143-153. 
  • Bounded Complexity of DNA Computing (with S. Karl and M. Saito), BioSystems 52 (1999), 63鈥72. 
  • DNA Hybridization, Shifts of Finite Type and Tiling of the Integers, in 鈥淕rammars and automata for string processing鈥, (Carlos Martin-Vide, ed.), pp. 369鈥380, Topics in Comput. Math., vol. 9, Taylor & Francis, London, 2003. 
  • A Conjugancy Invariant for Reducible Sofic Shifts and its Semigroup Characterizations (with E. Coven), Israel J. Math. 106 (1998), 221鈥249.

, Ph.D., Brown University, 1983; Distinguished University Professor.

Research Interests: Complex analysis, operator theory, potential theory, partial differential equations, harmonic functions, approximation theory, free boundary problems, gravitational microlensing.

Selected Publications

  • Symmetry and uniform approximation by analytic functions (with H. S. Shapiro), Proc. Amer. Math. Soc. 101 (1987), no. 3, 475鈥483. 
  • Dirichlet's problem when the data is an entire function, Bull. London Math. Soc. 24 (1992), 458鈥468. Contractive zero divisors in Bergman spaces (with P. Duren, H. S. Shapiro and C. Sundberg), Pacific J. Math. 157 (1993), no. 1, 37鈥56. 
  • Invariant subspaces in Bergman spaces and the biharmonic equation (with P. Duren, H. S. Shapiro and C. Sundberg), Mich. Math. J. 41 (1994), 247-259. 
  • On Dirichlet series with gaps (with J. M. Anderson and H. S. Shapiro), Revista Math. Iber. 2 (1995), no. 2, 453鈥476. 
  • Extending solutions of holomorphic partial differential equations across real hypersurfaces (with P. Ebenfelt and H. S. Shapiro), J. London Math. Soc. 57 (1998), no. 2, 411鈥432. 
  • On point-to-point reflection of harmonic functions across real analytic hypersurfaces in \(R^n\) (with P. Ebenfelt), J. d'Analyse 68 (1996), 145鈥182. 
  • Bohr's power series theorem in several variables (with H. P. Boas), Proc. Amer. Math. Soc. 125 (1997), no. 10, 2975鈥2979. 
  • Certain linear extremal problems in Bergman spaces of analytic functions (with M. Stessin), Indiana Univ. Math. J. 46 (1997), 933鈥974. 
  • On a maximal number of zeros of certain harmonic polynomials (with G. Swiatek), Proc. Amer. Math. Soc. 131 (2003), no. 2, 409鈥414. 
  • On the number of zeros of certain rational harmonic functions (with G. Neumann), Proc. Amer. Math. Soc. 134 (2006), no. 4, 1077鈥1085.

, Ph.D.,  University of Tennessee, Knoxville, 2000; Associate Professor

Research Interests: Operator and Function Theory, Mathematical Physics.

, Ph.D., SUNY-Binghamton, 1994; Associate Professor.

Research Interests: Geometric Methods in Group Theory, Combinatorial Group Theory, Hyperbolic Groups.

Selected Publications

  • Tilings of the plane, hyperbolic groups and small cancellation theory, Mem. Amer. Math. Soc. 154 (2001), no. 733.
  • Providing written feedback on students' mathematical arguments: proof validations of prospective secondary mathematics teachers (with S. K. Bleiler and D. R. Thompson), Journal of Mathematics Teacher Education 17(2) (2014), 105鈥127.
  • Counter machines and crystallographic structures (with N. Jonoska and G. McColm), Natural Computing 15(1) (2016), 97鈥113.
  • Multiple perspectives on collaborative teaching: Mathematicians, mathematics teacher educators, and students (with C. B茅n茅teau, S. K. Bleiler-Baxter, G. Kersaint, and D. R. Thompson), in L. West and M. Boston (Eds.), 鈥淎nnual Perspectives in Mathematics Education (APME): Reflective and Collaborative Processes to Improve Mathematics Teaching鈥, pp. 247鈥260, Reston, VA, National Council of Teachers of Mathematics, 2017.
  • On the prevalence of images in high school geometry textbooks (with M. Cannon), in Proceedings of the Second International Conference on Mathematics Textbooks, Rio de Janeiro, Brazil, 2018.
  • Common Visual Representations as a Source for Misconceptions of Pre-service Teachers in a Geometry Connection Course (with R. Sears), International Journal for Mathematics Teaching and Learning (Accepted).

, Ph.D., University of Chicago, 2007; Associate Professor.

Research Interests: Complex analysis, integrable systems, mathematical physics, asymptotic analysis, Riemann-Hilbert problems, orthogonal polynomials, various problems related to 2D Coulomb systems

Selected Publications

  • Topology of quadrature domains (with N. Makarov), J. Amer. Math. Soc. 29 (2016), 333鈥369. Remarks on Wilmshurst's theorem (with A. Lerario and E. Lundberg), Indiana Univ. Math. J. 64 (2015), 1153鈥1167. 
  • Strong asymptotics of the orthogonal polynomial with respect to a measure supported on the plane (with F. Balogh, M. Bertola and K. D. T-R McLaughlin), Comm. Pure Appl. Math. 68 (2015), no. 1, 112鈥172. 
  • First colonization of a hard-edge in random matrix theory (with M. Bertola), Const. Approx. 31 (2010), no. 2, 231鈥257. 
  • The boundary correlation function of fixed-to-free boundary-condition-changing operators in a square-lattice Ising model, J. Stat. Mech. (2007), P10011. 
  • Bubble break-off in Hele-Shaw flows: Singularities and integrable structures (with E. Bettelheim and P. Wiegmann), Physica D 219 (2006) 22鈥34.

 

, Ph.D., Academia Sinica, Beijing, 1990; Professor.

Research Interests: Applied Mathematics (soliton theory, integrability and applications of differential equations, Riemann-Hilbert problems and orthogonal polynomials, bifurcation and chaos); Mathematical Physics (symmetries and conservation laws, variational principles, Lie group method, Hamiltonian and bi-Hamiltonian theories, quantum and super-symmetric integrable systems); Symbolic Computation (symmetries and conservation laws, interactions of solitons and breathers, resonance and web structure of solitons, integrable decompositions, computer-assisted theorem proofs).

Selected Publications

  • A linear system arising from a polynomial problem and its applications [with B. Shekhtman], Chinese Annals of Mathematics, Series B, 23 (2002), 373鈥384. 
  • Semidirect sums of Lie algebras and discrete integrable couplings [with X. X. Xu and Y. Zhang], Journal of Mathematical Physics 47 (2006), 053501, 16 pp. 
  • Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions [with Y. You], Transactions of the American Mathematical Society 357 (2005), 1753鈥1778. 
    Complexiton solutions of the Toda lattice equation [with K. Maruno], Physica A 343 (2004), 219鈥37. 
  • Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems [with M. Blaszak], Journal of Geometry and Physics 47 (2003), 21鈥42. 
  • Binary nonlinearization of spectral problems of the perturbation AKNS systems [with R. G. Zhou], Chaos, Solitons & Fractals 13 (2002), 1451鈥1463. 
  • Binary symmetry constraints of \(\mathcal{N}\)-wave interaction equations in \(1+1\) and \(2+1\) dimensions [with Z. X. Zhou], Journal of Mathematical Physics 42 (2001), 4345鈥4382. 
  • Master symmetries from Lax operators for certain lattice soliton hierarchies [with K. M. Tamizhmani], Journal of the Physical Society of Japan 69 (2000), 351-361. 
  • Separation of variables for soliton equations via their binary constrained flows [with Y. B. Zeng], Journal of Mathematical Physics 40 (1999), 6526鈥6557. 
  • Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations [with B. Fuchssteiner], Journal of Mathematical Physics 40 (1999), 2400鈥2418.

, Ph.D., UCLA, 1986; Associate Professor.

Research Interests: My original interests were in mathematical logic and theoretical computer science, especially in logical expressibility, finite model theory, and descriptive and computational complexity. In order to deal with issues arising from logic, I applied tools from other areas, and consequently became active in finite and infinite combinatorics, especially in combinatorial games, Ramsey theory, random and extremal graph theory, and stochastic processes. Recently, I became active in applications of geometry to materials science and nanoscale science and technology; this involves mathematics (including Riemannian geometry and tiling theory, discrete and convex and computational geometry, geometric group theory and group representation theory, and category theory) and other natural sciences (including crystallography, molecular geometry, and related fields). Additionally, I am interested in pedagogy and related fields of applied psychology, in philosophy (especially the philosophy of science) and in academic politics (which as an academic field is usually classified as 鈥渆ducational leadership鈥 or 鈥渟ociology of science鈥).

Selected Publications

  • When is arithmetic possible?, Ann. Pure Appl. Logic 50:1 (1990), 29鈥51. 
  • A Ramseyian theorem for products of trees, J. Combinatorial Theory-A 57 (1991), 68鈥75. 
    Pebble games and subroutines in least fixed point logic, Inform. and Comp. 122:2 (1995), 201鈥220. 
  • A splitting inequality, Ramanujan Journal 2:4 (1998), 511鈥519. 
    Guarded Quantification in Least Fixed Point Logic, J. Logic, Language and Information 13 (2004), 61鈥110. 
  • A University's Dilemma in the Age of National Security (with Sherman Dorn), Thought & Action (Fall, 2005), 163鈥177. 
  • A Metaphor for Mathematics Education, Notices of the American Mathematical Society (April, 2007), 499鈥502. 
  • When is Betweenness Preserved? (with X.-D. Hou), Rocky Mountain J. Mathematics 38:1 (2008), 123鈥137. 
  • Is Logic Necessary? Logica Universalis 4:2 (2010), 241鈥254. 
  • Complexity Classes for Self-Assembling Flexible Tiles (with N. Jonoska), Theor. Comp. Sci. 410:4-5 (2009), 332鈥346. 
  • Crystal Engineering using a 鈥淭urtlebug鈥 Algorithm, a de novo approach to the design of binodal metal-organic frameworks (with W. E. Clark, M. Eddaoudi, L. Wojtas and M. Zaworotko), Crystal Growth & Design 11:9, (2011), 3686鈥3693. 
  • Prospects for Mathematical Crystallography, Acta Crystallographica A 70:2 (2014), 95鈥105. 
  • Counter machines and crystallographic structures (with N. Jonoska and M. Kraj膷evski), Natural Computing 15:1 (2016), 97鈥113.

, Ph.D. University of Zurich, 2015; Associate Professor.

Research Interests: Applied Algebra (Finite Fields, Cryptography, Coding Theory) and Number Theory (Density questions over Global Fields)

, Ph.D. Arizona State University, 2013; Associate Professor.

Research Interests: Extremal graph theory and probabilistic methods in combinatorics.

Selected Publications

  • Tiling directed graphs with tournaments (with A. Czygrinow, L. DeBiasio and A. Treglown), Forum of Mathematics, Sigma 6 (2018), E2. 
  • Triangle-tilings in graphs without large independent sets (with J. Balogh, A. McDowell and R. Mycroft) Combinatorics, Probability and Computing 27 (2018), 449鈥474. 
  • Transitive triangle-tilings in oriented graphs (with J. Balogh and A. Lo), Journal of Combinatorial Theory, Series B 124 (2017), 64鈥87. 
  • Sharpening an Ore-type version of the Corr谩di-Hajnal theorem (with H. A. Kierstead, A. Kostochka and E. Yeager), Abhandlungen aus dem Mathematischen Seminar der Universit盲t Hamburg 87 (2017), 299鈥335. 
  • Arbitrary orientations of Hamilton cycles in digraphs (with L. DeBiasio, D. K眉hn, D. Osthus and A. Taylor) SIAM Journal of Discrete Mathematics 29 (2015), 1553鈥1584.

, Ph.D., Emory University, 1999; Professor.

Research Interests: Extremal combinatorics, hypergraph regularity methods.

, Ph.D., University of New Hampshire, 1999; Professor.

Research Interests: C* Algebras and non-self-adjoint Operator Algebras, Theoretical Physics, Data Mining and Algorithms, Cryptography and Cryptology, Pedagody and Engineering

Selected Publications

  •  鈥淐entral Sequences in Subhomogeneous Unital C* Algebras,鈥 Don Hadwin and Hemant Pendharkar, to appear, Bulletin of Australian Math. Society, 2020.
  • 鈥淎n Experimental Investigation into the Practical Performance of Lattice Reduction Algorithm on Ideal Lattices,鈥 w/ Batson, et. al, SIAM Conference on Computational Science and Engineering, presentation, Atlanta 鈥 Supported by ONR 鈥 2017.
  • 鈥淪uitability of Lattices for Project Based Introduction to Cryptography,&rdqup; with Batson, et. al, Joint Mathematics Meeting, special section on Cryptology and cryptography presentation 鈥 Supported by ONR 鈥 2017.
  • 鈥淭echniques for minimizing area and power in test pattern generation," International Conference on Communication and Signal Processing (ICCSP), K. Jagtap, S. Rathkanthiwar, S. Kakde and H. Pendharkar, pp. 0429鈥0433, 2017.
  • 鈥淥n the Implementation of a Discrete Mathematics Course,鈥 Inroads, joint work of the SIGCSE sub-committee 鈥 2007 Data Mining and Algorithms.
  • 鈥淔requent pattern mining with preferences 鈥 Utility functions approach,鈥 E. Braynova and Hemant Pendharkar LNAI 3488, pp. 364-372, 2005.
  • 鈥淲ormhole Generated Physical Universe鈥, L. Choudhury and Hemant Pendharkar, Hadronic J. Vol. 24, issue 4, pp. 275鈥290, 2001.
  • 鈥淒erivations of Certain Operator Algebras,鈥 Jiankui Li and Hemant Pendharkar, International Journal of Mathematics, Vol. 24, pp. 345鈥351, 2000.

, Sc.D., Steklov Mathematics Institute, Moscow, 1983; Professor.

Research Interests: Analysis, theory of analytic functions, approximation theory (Pad茅 and rational approximation), potential theory, orthogonal polynomials.

Selected Publications

  • On the convergence of diagonal Pad茅 approximants, Math. USSR Sb. 33 (1977). 
  • On the convergence of simultaneous Pad茅 approximants for systems of functions of Markov type [with A. A. Gonchar], Proc. Steklov Inst. N3 (157). 
  • On the equilibrium problem for vector potentials [with A. A. Gonchar], Russian Math. Surveys 40 (1985). 
  • Rational approximations, orthogonal polynomials, and equilibrium distributions [with G. Lopez], Lecture Notes in Math. 1329 (1988). 
  • Equilibrium distributions and degree of rational approximations of analytic functions [with A. A. Gonchar], Math. USSR Sb. 62 (1989), 305-348. 
  • Strong asymptotics for orthogonal polynomials associated with exponential weights, in Methods of Approximation Theory in Complex Analysis and Mathematical Physics, (Moscow, 1992), NAUKA, pp. 71-97. 
  • Electrons on the sphere [with E. B. Saff and Y. M. Zhou], ICM Report 94-012, Dept. of Mathematics, USF.

J, Ph.D.,  University of Florida, 2013; Associate Professor

Research Interests: Machine Learning, Reproducing Kernel Hilbert Spaces, Approximation Theory, Cyber-physical Systems Verification, Fractional Order Partial and Ordinary Differential Equations, Operator Theory and Functional Analysis, Optimal Control Theory, Adaptive Dynamic Programming, Densely Defined Operators, and The History of Mathematics.

, Ph.D., University of Texas at Austin, 1990; Professor Emeritus.

Research Interests: Knot theory, low dimensional topology, related algebraic structures, and applications to DNA recombination.

Selected Publications

  • Surfaces in 4-space [with J. S. Carter and S. Kamada], Encyclopedia of Mathematical Sciences, vol. 142, Springer-Verlag, 2004. 
  • Knotted Surfaces and Their Diagrams [with J. S. Carter], Mathematical Surveys and Monographs, volume 55, American Mathematical Society, 1998. 
  • Classical and quantum \(6j\) symbols [with J. S. Carter and D. E. Flath], Mathematical Notes, vol. 43, Princeton University Press, 1993.

, Ph.D., Texas A&M University, 2009; Associate Professor.

Research Interests: Geometric and combinatorial group theory. Groups acting on rooted trees: self-similar, generated by automata, iterated monodromy groups, contracting and branch groups. Algorithmic aspects of self-similar groups. Developing software for computations in group theory. \(p\)-adic dynamics. Thompson's groups.

Selected Publications

  • "Affine Automorphisms of Rooted Trees" (with S. Sidki), Geometriae Dedicata 183 (2016), 195鈥213.
  • "Orbit automata as a new tool to attack the order problem in automaton groups" (with Ines Klimann and Matthieu Picantin), Journal of Algebra 445 (2016), 433鈥457.
  • "Ergodic decomposition of group actions on rooted trees" (with R. Grigorchuk), Proceedings of the Steklov Institute of Mathematics 292 (2016), no. 1, 94鈥111.
  • "An Example of an Automatic Graph of Intermediate Growth" (with A. Miasnikov), Annals of Pure and Applied Logic 166 (2015), no. 10, 1037鈥1048.
  • "Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set", Geometriae Dedicata, V.175 (2015), 355鈥372.
  • "On the geometry of the edge splitting complex" (with L. Sabalka), Groups, Geometry, and Dynamics, 8 (2014), no. 2, 565鈥598.
  • "Automata generating free products of groups of order 2" (with Y. Vorobets), Journal of Algebra, V.336 (2011), Issue 1, 53鈥66.
  • Package AutomGrp for computations in groups and semigroups generated by automata or given by wreath recursion for GAP system (joint with Y. Muntyan). Accepted Package.

, Ph.D., Kent State University, 1980; Professor.

Research Interests: Mathematics in general (Classical and Abstract Analysis, Approximation Theory, Discrete Mathematics, Linear Algebra in particular). Meaning of life, Psychology, Creative Writing and a bunch of other stuff. Anything that's fun.

Selected Publications

  • On the Divergence of Polynomial Interpolation, Constr. Approx. 17 (2001). 
  • On Interpolation by and Banach Spaces of Polynomials, Erd枚s Memorial Volume (2001). 
  • On Density Principle for Rational Functions, Numerical Algorithms 25 (2000). 
  • A Two-Dimensional Hahn-Banach Theorem, Proc. of AMS 129 (2000), (with B. L. Chalmers). 
  • Linear Discrete Operators on the Disk Algebra, Proc. Amer. Math. Soc. 129 (2000), (with I. Ivanov). 
  • On Archimidian Ordered Vector Spaces and a Characterization of Simplices, Proc. AMS 116 (1992), (with G. Gierz). 
  • Science Fiction of Distance Learning, preprint.

, Ph.D., Jagiellonian University, 2001; Professor.

Research Interests: Approximation Theory and Functional Analysis. In particular I am interested in Minimal Projections and \(L_p\) spaces.

Selected Publications

  • Chalmers-Metcalf Operator and Uniqueness of Minimal projections, J. Approx. Theory 148 (2007), 71-91 (with