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), 99–105. 
  • Some coefficient estimates for \(H^P\) functions (with B. Korenblum), “Complex Analysis and Dynamical Systems”, Contemporary Mathematics, vol. 364, 2004, pp. 5–14. 
  • Remarks on the Bohr phenomenon (with A. Dahlner and D. Khavinson), Computational Methods and Function Theory 4 (2004), no. 1, 1–19. 
  • 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), 59–86. 
  • The isoperimetric inequality via approximation theory and free boundary problems(with D. Khavinson), Computational Methods and Function Theory 6 (2006), no. 2, 253–274.

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

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

, Ph.D., Institute of Mathematics of Academy of Sciences of Armenia, 1987; Associate 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, 813–816. 
  • A theorem of Lohwater and Piranian, Proc. Amer. Math. Soc. 144 (2016), no. 9, 3919–3920. 
  • A converse to a theorem of Salem and Zygmund (with V. Totik), Bull. Sci. Math. 140 (2016), no. 3, 260–272. 
  • On the zero-free polynomial approximation problem, J. Approx. Theory 205 (2016), 60–63. 
  • Weak-star convergence and a polynomial approximation problem, Results Math. 69 (2016), no. 1-2, 257–262. 
  • On the peak points, Complex Var. Elliptic Equ. 60 (2015), no. 11, 1475–1479. 
  • On a polynomial approximation problem, J. Approx. Theory 162 (2010), no. 4, 717–722. 
  • 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, 245–254.

, 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), 166–187.
  • 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, 4787–4802.
  • On the classification of topological quandles (with Z. Chend and B. Shekhtman), Topology Appl. 248 (2018), 64–74.
  • 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, 5155–5177.
  • Pretzel knots and \(q\)-series (with M. Hajij), Osaka J. Math. 54 (2017), no. 2, 363–381. The colored Jones polynomial of singular knots (with K. Bataineh and M. Hajij), New York J. Math. 22 (2016), 1439–1456.
  • Foundations of topological racks and quandles (with E. Moutuou), J. Knot Theory Ramifications 25 (2016), no. 3, 1640002, 17 pp.
  • Quandles—an 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), 366–378. 
  • \(\mathrm{AGL}(m,2)\) acting on \(R(r,m)/R(s,m)\), J. Algebra 171 (1995), 921–938. 
  • Results on bent functions (with P. Langevin), J. Combin. Theory A 80 (1997), 232–246. 
  • A generalization of an addition theorem of Kneser (with K. H. Leung and Q. Xiang), J. Number Theory 97 (2002), 1–9. 
  • Enumeration of isomorphism classes of extensions of \(p\)-adic fields (with K. Keating), J. Number Theory 104 (2004), 14–61.
  • Solution to a problem of S. Payne, Proc. Amer. Math. Soc. 132 (2004), 1–8. 
  • A note on the proof of a theorem of Katz, Finite Fields Appl. 11 (2005), 316–319. 
  • Reversed Dickson permutation polynomials over finite fields (with G. L. Mullen, J. A. Sellers and J. L. Yucas), Finite Fields Appl. 15(2009), 748–773. 
  • Automorphism groups of Alexander quandles, J. Algebra 344 (2011), 373–385. 
  • Connected quandles associated with pointed abelian groups (with W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman), Pacific J. Math. 264 (2013), 31–60. 
  • A new approach to permutation polynomials over finite fields, II (with N. Fernando and S. D. Lappano), Finite Fields Appl. 22 (2013), 122–158. 
  • Permutation polynomials over finite fields—a survey of recent advances, Finite Fields Appl. 32 (2015), 82–119. 
  • Switchings of semifield multiplications (with F. Ozbudak and Y. Zhou), Des. Codes Cryptogr. 80 (2016), 217–239. 
  • On global \(\mathcal{P}\)-forms, J. Number Theory 160 (2016), 307–325. 
  • Polynomials meeting Ax's bound, Acta Arith. 176 (2016), 65–80. 
  • Proof of a conjecture on monomial graphs (with S. D. Lappano and F. Lazebnik), Finite Fields Appl. 43 (2017), 42–68.

, 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), 63–72. 
  • DNA Hybridization, Shifts of Finite Type and Tiling of the Integers, in “Grammars and automata for string processing”, (Carlos Martin-Vide, ed.), pp. 369–380, 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), 221–249.

, 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, 475–483. 
  • Dirichlet's problem when the data is an entire function, Bull. London Math. Soc. 24 (1992), 458–468. Contractive zero divisors in Bergman spaces (with P. Duren, H. S. Shapiro and C. Sundberg), Pacific J. Math. 157 (1993), no. 1, 37–56. 
  • 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, 453–476. 
  • 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, 411–432. 
  • On point-to-point reflection of harmonic functions across real analytic hypersurfaces in \(R^n\) (with P. Ebenfelt), J. d'Analyse 68 (1996), 145–182. 
  • Bohr's power series theorem in several variables (with H. P. Boas), Proc. Amer. Math. Soc. 125 (1997), no. 10, 2975–2979. 
  • Certain linear extremal problems in Bergman spaces of analytic functions (with M. Stessin), Indiana Univ. Math. J. 46 (1997), 933–974. 
  • On a maximal number of zeros of certain harmonic polynomials (with G. Swiatek), Proc. Amer. Math. Soc. 131 (2003), no. 2, 409–414. 
  • On the number of zeros of certain rational harmonic functions (with G. Neumann), Proc. Amer. Math. Soc. 134 (2006), no. 4, 1077–1085.

, 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), 105–127.
  • Counter machines and crystallographic structures (with N. Jonoska and G. McColm), Natural Computing 15(1) (2016), 97–113.
  • Multiple perspectives on collaborative teaching: Mathematicians, mathematics teacher educators, and students (with C. Bénéteau, S. K. Bleiler-Baxter, G. Kersaint, and D. R. Thompson), in L. West and M. Boston (Eds.), “Annual Perspectives in Mathematics Education (APME): Reflective and Collaborative Processes to Improve Mathematics Teaching”, pp. 247–260, 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; Assistant 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), 333–369. Remarks on Wilmshurst's theorem (with A. Lerario and E. Lundberg), Indiana Univ. Math. J. 64 (2015), 1153–1167. 
  • 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, 112–172. 
  • First colonization of a hard-edge in random matrix theory (with M. Bertola), Const. Approx. 31 (2010), no. 2, 231–257. 
  • 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) 22–34.

, Ph.D., University of Houston, 2005; Associate Professor.

Research Interests: Mathematical modeling, dynamical systems, nonlinear dynamics of networks, and optimal control.

Zhenkun Li, Ph.D., MIT, 2020; Assistant Professor.

Research Interests: Low dimensional topology, knot theory, Gauge theory, Floer homology.

Selected Publications

  • Small Dehn surgeries and \(\mathrm{SU}(2)\) (with J. Baldwin, S. Sivek and F. Ye), Geom. Topol. (2024), to appear.
  • Sutured instanton Floer homology and Heegaard diagrams (with J. Baldwin and F. Ye), Compos. Math. (2023), to appear.
  • Instanton Floer homology, sutures and Euler characteristics (with F. Ye), Quantum Topol. (2023), to appear.
  • Instanton Floer homology, sutures, and Heegaard diagrams (with F. Ye), J. Topol. 15 (2022), 39-107.
  • Decomposing sutured monopole and instanton Floer homologies (with S. Ghosh), Sel. Math. New Ser. (2023), to appear.

, 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), 373–384. 
  • 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), 1753–1778. 
    Complexiton solutions of the Toda lattice equation [with K. Maruno], Physica A 343 (2004), 219–37. 
  • Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems [with M. Blaszak], Journal of Geometry and Physics 47 (2003), 21–42. 
  • Binary nonlinearization of spectral problems of the perturbation AKNS systems [with R. G. Zhou], Chaos, Solitons & Fractals 13 (2002), 1451–1463. 
  • 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), 4345–4382. 
  • 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), 6526–6557. 
  • Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations [with B. Fuchssteiner], Journal of Mathematical Physics 40 (1999), 2400–2418.

, 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 “educational leadership” or “sociology of science”).

Selected Publications

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

, Ph.D. University of Zurich, 2015; Assistant 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), 449–474. 
  • Transitive triangle-tilings in oriented graphs (with J. Balogh and A. Lo), Journal of Combinatorial Theory, Series B 124 (2017), 64–87. 
  • Sharpening an Ore-type version of the Corrádi-Hajnal theorem (with H. A. Kierstead, A. Kostochka and E. Yeager), Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 87 (2017), 299–335. 
  • Arbitrary orientations of Hamilton cycles in digraphs (with L. DeBiasio, D. Kühn, D. Osthus and A. Taylor) SIAM Journal of Discrete Mathematics 29 (2015), 1553–1584.

, 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

  •  “Central Sequences in Subhomogeneous Unital C* Algebras,” Don Hadwin and Hemant Pendharkar, to appear, Bulletin of Australian Math. Society, 2020.
  • “An Experimental Investigation into the Practical Performance of Lattice Reduction Algorithm on Ideal Lattices,” w/ Batson, et. al, SIAM Conference on Computational Science and Engineering, presentation, Atlanta — Supported by ONR — 2017.
  • “Suitability of Lattices for Project Based Introduction to Cryptography,&rdqup; with Batson, et. al, Joint Mathematics Meeting, special section on Cryptology and cryptography presentation — Supported by ONR — 2017.
  • “Techniques 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. 0429–0433, 2017.
  • “On the Implementation of a Discrete Mathematics Course,” Inroads, joint work of the SIGCSE sub-committee — 2007 Data Mining and Algorithms.
  • “Frequent pattern mining with preferences — Utility functions approach,” E. Braynova and Hemant Pendharkar LNAI 3488, pp. 364-372, 2005.
  • “Wormhole Generated Physical Universe”, L. Choudhury and Hemant Pendharkar, Hadronic J. Vol. 24, issue 4, pp. 275–290, 2001.
  • “Derivations of Certain Operator Algebras,” Jiankui Li and Hemant Pendharkar, International Journal of Mathematics, Vol. 24, pp. 345–351, 2000.

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

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

Selected Publications

  • On the convergence of diagonal Padé approximants, Math. USSR Sb. 33 (1977). 
  • On the convergence of simultaneous Padé 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, ŷƬ.

J, Ph.D.,  University of Florida, 2013; Assistant 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.

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), 195–213.
  • "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), 433–457.
  • "Ergodic decomposition of group actions on rooted trees" (with R. Grigorchuk), Proceedings of the Steklov Institute of Mathematics 292 (2016), no. 1, 94–111.
  • "An Example of an Automatic Graph of Intermediate Growth" (with A. Miasnikov), Annals of Pure and Applied Logic 166 (2015), no. 10, 1037–1048.
  • "Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set", Geometriae Dedicata, V.175 (2015), 355–372.
  • "On the geometry of the edge splitting complex" (with L. Sabalka), Groups, Geometry, and Dynamics, 8 (2014), no. 2, 565–598.
  • "Automata generating free products of groups of order 2" (with Y. Vorobets), Journal of Algebra, V.336 (2011), Issue 1, 53–66.
  • 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, Erdös 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; Associate 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 G. Lewicki).
  • Norming Points and Unique Minimality of Otrhogonal Projections, Abstract and Applied Analysis, 2006, Art. ID 42305, 1-17, (with B. Shekhtman). 
  • Uniqueness of Minimal Projections onto Two-Dimensional Subspaces, Studia Mathematica 168 (2005), 273-284 (with B. Shekhtman). 
  • The Uniqueness of Norm-One Projection in James-type Spaces, J. Approx. Theory 100 (1999), 73-93.

, Ph.D., University of Chicago, 2004; Associate Professor.

Research Interests: Integrable nonlinear differential equations, stochastic processes and harmonic analysis, biorthogonal polynomials and approximation theory, mathematical physics.

Selected Publications

  • Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painlevé I transcendent, with S-Y. Lee and P. Wiegmann, Physica D (2011). 
  • Lemniscates are destroyed by Laplacian growth, with D. Khavinson, M. Mineev-Weinstein and M. Putinar, Mathematical Research Letters 17 2 (2010), 337. 
  • Random matrix theory in 2D, Laplacian growth, and operator theory, with M. Mineev-Weinstein and M. Putinar, J. Phys. A: Math. Theor. 41 (2008), 263001. 
  • Normal matrix ensemble as a growth problem, with E. Bettelheim, O. Agam, A. Zabrodin and P. B. Wiegmann, Nucl. Phys. B 704 (2005) 407.

, Ph.D., Mathematics, Claremont Graduate School, 1997; Ph.D., Computer Science, North Carolina State University, 2007; Professor.

Research Interests: Computer and networking security including cryptography and its performance evaluation with applications to cloud computing, big-data computing, green computing, mobile/smartphone computing, wireless sensor networks, web applications, health care information systems, and cyber physical systems (power grids and GIS).

Statistics Faculty Research

, Ph.D., University of Rhode Island, 1971; Professor.

Research Interests: Dynamic Reliability/Survival Analysis under the Influence of Internal and External Intervention Processes and Control; Stochastic Modeling, Methods and Analysis of Dynamic Processes in Biological, Chemical, Engineering, Financial, Medical, Military, Physical and Social Sciences; Time Series Analysis and Applications; State and Parameter Estimation Problems in Statistical and Modeling Analysis; Multivariate/Large-Scale Systems Analysis; Stochastic Modeling of Network Dynamic Processes; Multi-Agent, Multi-Cultural, and Multi-Market/Financial Dynamic Systems; Approximations, Statistical Analysis, Conceptual and Computational Algorithms; Deterministic, Hereditary and Stochastic Qualitative and Quantitative Analysis of Dynamic Systems; Stochastic Hybrid Dynamic Processes under Environmental Structural Perturbations.

Selected Publications

  • Stochastic Modeling, Analysis and Applications of the Solar Cycle Dynamic Process (with D. C. Turner), The Astrophysical Journal 855 (2018), no. 6, 1–16.
  • Stochastic Hybrid Dynamic Multicultural Social Networks (with K. B. Hilton) Transactions on Networks and Communications 5 (2017), no. 5, 1–23.
  • Option Pricing with a Levy-type Stochastic Dynamic Model for Stock Price Process under Semi-Markovian Structural Perturbations (with P. Assonken), Int. J. Theor. Appl. Finance 18 (2015), 1–72.
  • Agent-Based Modeling Simulation under Local Network Externality (with A. Paothong), J. Econ. Interact. and Coord. 9 (2014), 1–26.
  • Global Properties of a two-scale stochastic Human Epidemic Dynamic Model (with D. Wanduku), Nonlinear Anal.-Real 13 (2012), no. 2, 794–816.
  • Stochastic Fractional Differential Equations: Modeling, Methods and Analysis (with J.-C. Pedjeu), Chaos, Solitons Fractals 45 (2012), 279–293.
  • Stochastic Hybrid Systems with Non-homogeneous and Boundary Jumps (with D. P. Siu), Nonlinear Anal.-Hybri. 5 (2011), 591–602.
  • A Two-scale Network Dynamic Model for Human Mobility Process (with Divine Wanduku), Mathematical Biosciences 229 (2011), 1–15.
  • Stochastic Modeling Analysis and Applications (with A. G. Ladde), International Encyclopedia of Statistical Sciences, (Miodrag Lovric, ed.), Springer, 2010, pp. 1526–1531.
  • Collective behavior of multi-agent network dynamic systems under internal and external random perturbations (with J. Chandra), Nonlinear Anal.-Real 11 (2010), 1330–1344.
  • Development of modified Geometric Brownian Motion models by using stock price data and basic statistics (with Ling Wu), Nonlinear Anal.-Theor. 71 (2009), e1203–e1208.
  • Modeling Hybrid Network Dynamics under Random Perturbations (with A. Korzeniowski), Nonlinear Anal.-Hybri. 3, (2009), 143–149.
  • Qualitative Properties of Stochastic Iterative Processes under Markovian Structural Perturbations (with B. L. Griffin), Math. Comput. Simulations 67 (2004), 181–200.
  • Convergence and Stability of Distributed Stochastic Iterative Processes (with D. D. Siljak), IEEE Trans. Automat. Control 35 (1990), 665–672.
  • Processing of Prefiltered GPS Data (with M. S. Smith), IEEE Trans. Aero. Elec. Sys. 25 (1989), 711–728.
  • Multiplex Control Systems: Stochastic Stability and Dynamic Reliability (with D. D. Siljak), Int. J. of Contr. 28 (1983).
  • Variational Comparison Theorem and Perturbations of Nonlinear Systems, Proc. Amer. Mat. Soc. 52 (1975), 165–187.
  • Stochastic Versus Deterministic Systems of Differential equations (with M. Sambandham), Marcel Dekker, NY, 2004.
  • Oscillation Theory of Differential Equations with Deviating Arguments (with V. Lakshmikantham and B. G. Zhang), Marcel Dekker, Inc., New York, 1987.
  • Monotone Iterative Techniques for Nonlinear Differential Equations, (with V. Lakshmikantham and A. Vatsala), Pitman Publishing, Inc., Marshfield, MA 1985.
  • Random Differential Inequalities (with V. Lakshmikantham), Academic Press, New York, 1980.

, Ph.D., Iowa State University, 2009; Associate Professor.

Research Interests: Reliability analysis, design of experiment, response surface methodology, survey sample design and methodology, multiple objective optimization, statistical engineering.

Selected Publications

  • Optimization of Designed Experiments based on Multiple Criteria Utilizing Pareto Frontier (with C. M. Anderson-Cook and T. J. Robinson), Technometrics 53 (2011), 353–365. 
  • A Case Study on Selecting a Best Allocation of New Data for Improving the Estimation Precision of System and Sub-System Reliability using Pareto Fronts (with J. L. Chapman and C. M. Anderson-Cook), Technometrics 55:4 (2013), 473–487. 
  • Optimal Designed Experiments Using a Pareto Front Search for More Focused Desirability Function Weights (with C. M. Anderson-Cook and D. Lin), Computational Statistics and Data Analysis 71 (2014), 1178–1192. 
  • Incorporating Response Variability into Pareto Front Optimization (with J. L. Chapman and C. M. Anderson-Cook), Computers and Industrial Engineering 76 (2014), 253–267. 
  • Multiple Response Optimization for Higher Dimensions in Factors and Responses (with J. L. Chapman and C. M. Anderson-Cook), Quality Reliability Engineering International. 
  • Multiple Objective Optimization in Reliability Demonstration Test (with M. Li and C. M. Anderson-Cook), Journal of Quality Technology 48:4 (2016), 326–342.

, Ph.D., Brown University, 1987; Professor.

Research Interests: Stochastic control problems; approximate solutions using weak convergence or Martingale techniques; computational techniques to obtain optimal controls; learning algorithms, which may arise in the context of artificial intelligence, via stochastic approximation techniques; applied problems involving stochastic calculus and distributed parameter systems; Software reliability, Digital communications, Applications of Wavelet analysis in Statistics and Signal Processing.

Selected Publications

  • Optimal and approximately optimal control policies or queues in heavy traffic (with H. J. Kushner), SIAM J. Opt. and Control 27 (1989), 1293–1318. 
  • Asymptotic behavior of a hierarchical system of learning automata (with M. A. L. Thathachar), Information Sciences 35 (1985), 91–110. 
  • Nearly optimal state feedback controls for delay differential equations with a small parameter (with G. Yin), J. Math. Anal. Appl. 172 (1993), no. 2, 480–499. 
  • Stochastic differential games with a small parameter, Stochastics and Stochastics Reports 43 (1993), 73–91. 
  • Convergence problems for an impulsively and singularly controlled system, Nonlinear Analysis, Theory, Methods & Applications 30 (1997), no. 1, 223–232. 
  • Wavelet Framework for joint Filtering and Compression based on Moments(with R. Chandramouli and S. Gomatam), submitted to Signal Processing, 1999. 
  • Stochastic differential games and applications, book chapter, to appear in “Handbook of Stochastic Analysis and Applications,” (D. Kannan and V. Lakshmikantham, eds.), Marcel Dekker, Inc., 2000.

, Ph.D., University of Connecticut, 1968; Distinguished University Professor.

Research Interests: AI-BIG DATA statistical analysis and modeling. Cybersecurity/vulnerability — Stochastic Analysis and Modeling of Network Systems. Machine Learning, Deep Learning Data Analytics, Neural Network, Random Forest in Analyzing and Modeling Health Systems — brain, lung, prostate, ovarian, breast cancers. Parametric, nonparametric, Bayesian Reliability and Survival Analysis. Nonlinear Statistical Models for Social Sciences. Global Warming — causes, forecasting models, world-wide comparisons, regional clusterings. Analysis and Clustering of Nonstationary signals in Environmental, Engineering and Health Sciences. Radar Ground Detection systems driven by nonparametric-Time series algorithms. AI-Machine Learning Models for Finance, Capital Asset Selection and Allocation Analysis, and cybersecurity issues. Structuring and evaluation of diversified financial portfolios.

Selected Publications

  • Maximum Likelihood Estimation for the Generalized Pareto Distribution with Goodness-of-fit Test and Censored Data (with Minh Pham), J. Mod. Appl. Stat. Methods (2017), submitted.
  • Active and Dynamic Approaches for Clustering Time Dependent Lag Information: Lag Target Time Series Clustering and Multi-factor Time Series Clustering (with Doo Young Kim), J. Stat. Theory Appl. 17 (2018), no. 3, 462–477.
  • Time Series Predictive Modeling of Vulnerabilities Using Desktop Operating System Using Linear and Non-linear Approach (with N. R. Pokhrel and H. Rodrigo), J. Inf. Secur. 8 (2017), no. 4, 362–382.
  • Non-homogeneous Stochastic Model for Cybersecurity Predictions (with P. K. Kaluarachchi and S. M. Rajasooriya), J. Inf. Secur. 9 (2018), no. 1, 12–24.
  • Artificial Neural Network Model for Predicting Lung Cancer Survival (with H. Rodrigo), J. Data Anal. Inf. Proc. 5 (2017), no. 1, 33–47.
  • A Stochastic Predictive Model to Determine Overall Network Security Risk Using Markovian Process (with N. R. Pokhrel), J. Inf. Secur. 8 (2017), no. 2, 91–105.
  • Common Spatial Pattern Method for Real-time Eye State Identification by Using Electroencephalogram Signals (with A. Saghafi and H. Farhidzadeh), IET Sig. Proc. 11 (2017), no. 8, 936–941.
  • Statistical Forecasting Models of Atmospheric Carbon Dioxide and Temperature in the Middle East (with M. Habadi), J. Geosci. Env. Protect. 5 (2017), no. 10, 11–21.
  • Statistical Significance of Fossil Fuels for Contributing to Atmospheric Carbon Dioxide in South Korea, and Comparisons with USA and EU (with D. Y. Kim), J. Appl. Stat. Sci. 21 (2017), no. 4, 345–355.
  • Cyber Security: Nonlinear Stochastic Models for Predicting the Exploitability (with S. M. Rajasooriya and P. K. Kaluarachchi), J. Inf. Secur. 8 (2017), no. 2, 125–140.
  • Improved Parameter Estimation of Time Dependent Kernel Density by Using Artificial Neural Networks (with A. Saghafi and X. Wang), J. Fin. Data Sci. 4 (2018), no. 4.
  • Random Eye State Change Detection in Real-time Using EEG Signals (with A. Saghafi, M. Goudarzi, and H. Farhidzadeh), Expert Syst. Appl. 72 (2017), no. 15, 42–48.
  • Bayesian Modeling of Nonlinear Poisson Regression with Artificial Neural Networks (with H. Rodrigo), Neural Comput. Appl. (2018), submitted.
  • Risk Rank Analysis Methods for Vulnerabilities in a Network System (with P. K. Kaluarachchi and S. M. Rajasooriya), J. Inf. Secur. (2018), submitted.
  • On Heredity Factors of Parkinson's Disease: A Parametric and Bayesian Analysis (with A. Saghafi and R. D. Wooten), Adv. Parkinson Dis. 7 (2018), no. 3, 31–42.
  • Differential Equation Modeling of Carbon Dioxide Emissions Using Functional Linear Regression (with N. Khanal and R. Kafle), J. Appl. Stat. (2018), 1–14.
  • A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis (with M. Perera), Journal of Advances in Breast Cancer Research 7 (2018), no. 1, 65–89.
  • Modeling Breast Cancer Survival Data When the Proportional Hazard Assumption is in Violation (with M. Perera), J. Mod. Appl. Stat. Meth. (2018), submitted.
  • Reliability Models Using the Composite Generalizers of Weibull Distribution (with G. Aryal, K. Pokhrel, and N. Khanal), Comm. Stat. Appl. Meth. (2018), submitted.
  • Forecasting Models and Their Applications to Exchange and Economic Traded Funds (with V. Ganesh and M. Kotarinos), Int. Journal of Math Sciences and Business (2018), submitted.
  • Multi-Level Time Series Clustering: Issues with Traditional Risk Management Framework (with M. Kotarinos, D. Kim), Proc. American Statistical Assoc. (2018), submitted.
  • Bayesian Artificial Neural Networks (with H. Rodrigo), Pattern Recognition (2018), submitted.
  • Modeling Breast Cancer Survival Data when the Proportional Hazards Assumption is in Violation (with M. Devamitta Perera), J. Mod. Appl. Stat. Methods (2018), submitted.