Faculty Research Interests

LISTED BELOW ARE THE REGULAR FACULTY of the Mathematics Department, along with selected recent publications.

In addition to the regular faculty, the department has a number of Whyburn Research Instructors and visiting faculty from other universities in residence in any given year. Colloquia and seminars also bring in experts from other universities to lecture on important recent advances.

For information on the research interests of the faculty, as well as links to Math Reviews of all faculty publications, please see:

ABDELMALEK ABDESSELAM   [Home Page]
Assistant Professor; Ph.D., Ecole Polytechnique, 1997. Mathematical physics, combinatorics and representation theory.

• A complete renormalization group trajectory between two fixed points, Comm. Math. Phys. 276(3) (2007), 727-772.
  preprint version arXiv:math-ph/0610018
• Brill-Gordan loci, transvectants and an analogue of the Foulkes conjecture, Adv. Math. 208(2) (2007), 491-520 (with J. Chipalkatti).
  preprint version arXiv:math.AG/0411110

PETER ABRAMENKO   [Home Page]
Professor; Ph.D. and Habilitation, University of Frankfurt/Main, 1987 and 1995. Group theory and geometry.

• Twin Buildings and Applications to S-Arithmetic Groups, Lecture Notes in Mathematics 1641, Springer (1996).
• Buildings: Theory and Applications, Graduate Texts in Mathematics 248, Springer (2008) (with Ken Brown).

GREGORY ARONE   [Home Page]
Professor; Ph.D., Brown University, 1993. Topology.

• Calculus of functors, operad formality, and rational homology of embedding spaces, Acta Mathematica 153-198 (with P. Lambrechts and I. Volic).
  arxiv math/0607486
• Filtered spectra arising from permutative categories, Crelle's Math Journal 604 (2007), 73-136 (with Kathryn Lesh).

MIKHAIL ERSHOV   [Home Page]
Assistant Professor; Ph.D., Yale University, 2005. Group theory.

• The Nottingham group is finitely presented, J. London Math. Soc. 71(2) (2005), 362-378.
• Finite presentability of SL₁(D), Israel Journal of Math. 158 (2007), 297-347.

CHRISTIAN GROMOLL   [Home Page]
Assistant Professor; Ph.D., University of California, San Diego, 2001. Probability, stochastic processes and their applications.

• The fluid limit of a heavily loaded processor sharing queue, Annals of Applied Probability 12 (2002), 797-859 (with A. L. Puha and R. J. Williams).
• Diffusion approximation of a processor sharing queue in heavy traffic, Annals of Applied Probability 14 (2004), 555-611.

ZORAN GRUJIC   [Home Page]
Associate Professor; Ph.D., Indiana University, 1998. Nonlinear PDE's and fluid dynamics.

• Space analyticity for the Navier-Stokes and related equations with initial data in L^p, J. Funct. Anal. 152 (1998), 447-466 (with I. Kukavica).
• The geometric structure of the super-level sets and regularity for 3D Navier-Stokes equations, Indiana Univ. Math. J., 50(3) (2001), 1309-1317.

IRA W. HERBST   [Home Page]
Professor; Ph.D., University of California, Berkeley, 1971. Mathematical physics.

• Absence of ground states for a class of translation invariant models of non-relativistic QED, Comm. Math. Phys. 279 (2008), 769-787 (with David Hasler).
  arXiv:math-ph/0702096
• On the lifetime of quasi-stationary states in non-relativistic QED, to appear in Ann. Henri Poincaré (with D. Hasler and M. Huber).
  arXiv:0709.3856

MICHAEL A. HILL
Assistant Professor; Ph.D., Massachusetts Institute of Technology, Cambridge, 2006. Topology.

JEFFREY J. HOLT
Associate Professor; Ph.D., University of Texas, 1993. Analytic number theory.

• The Beurling-Selberg extremal functions for a ball in Euclidean space, Duke Math. J. 83, no. 1 (1996), 203-247 (with J. D. Vaaler).
• On the solutions to φ(u) = φ(n+k), Proc. Int. Conf. on Number Theory in Honor of Andrzej Schinzel (J. Kowalski, ed.), Walter de Gruyter, Berlin (1998), 867-882 (with C. Pomerance and S. W. Graham).

JOHN Z. IMBRIE   [Home Page]
Professor; Ph.D., Harvard University, 1980. Physics.

• Branched polymers and dimensional reduction, Annals of Mathematics, 158 (2003), 1019-1039 (with D. Brydges).
  arXiv:math-ph/0107005
• End-to-end distance from the Green's Function for a hierarchical self-avoiding walk in four dimensions, Commun. Math. Phys. 239 (2003), 549-584 (with D. Brydges).
  arXiv:math-ph/0205027

THOMAS L. KRIETE   [Home Page]
Professor; Ph.D., University of Virginia, 1968. Operator theory.

• Toeplitz-composition C*-algebras, J. Operator Theory, 359(6) (2007), 2915-2944 (with Barbara MacCluer and Jennifer Moorhouse).
  http://arxiv.org/abs/math.OA/0608445
• Linear relations in the Calkin algebra for composition operators, Transactions Amer. Math. Soc., to appear (with Jennifer Moorhouse).
  http://arxiv.org/abs/math.FA/0608466

SLAVA KRUSHKAL   [Home Page]
Professor; Ph.D., University of California-San Diego, 1996. Low-dimensional topology and geometry.

• A counterexample to the strong version of Freedman's conjecture, Annals of Mathematics 168 (2008), 675-693.
  Preprint version: http://arxiv.org/PS_cache/math/pdf/0610/0610865v2.pdf (.pdf)
• Tutte chromatic identities from the Temperley-Lieb algebra, Geometry and Topology 13 (2009), 709-741 (with Paul Fendley).
  Preprint version: http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0016v3.pdf (.pdf)

NICHOLAS J. KUHN   [Home Page]
Professor; Ph.D., University of Chicago, 1980. Algebraic topology and representation theory.

• Localization of Andre--Quillen--Goodwillie towers, and the periodic homology of infinite loopspaces, Advances in Math. 201 (2006), 318-378.
• Primitives and central detection numbers in group cohomology, Advances in Math. 216 (2007), 387-442.

IRENA LASIECKA   [Home Page]
Professor; Ph.D., University of Warsaw, Poland, 1975. Nonlinear partial differential equations, mathematical control theory, applied mathematics.

• Mathematical Control Theory of Coupled PDE's, CBMS-NSF Conference Series in Applied Mathematics, SIAM, Philadelphia, 2002.
• Long time behavior of second order evolution equations with nonlinear damping (with I. Chueshov), Memoires of AMS, vol. 912, 2008.

BARBARA D. MacCLUER   [Home Page]
Professor; Ph.D., Michigan State University, 1983. Function theory and operator theory.

• Composition Operators on Spaces of Analytic Functions, Boca Raton: CRC Press, 1995 (with C. Cowen).
• Toeplitz-composition C^*-algebras, J. Operator Theory 135-156 (with T. Kriete and J. Moorhouse).

THOMAS E. MARK   [Home Page]
Assistant Professor; Ph.D., Michigan State University, 2000. Low-dimensional topology and geometry; gauge theory.

• Product formulae for Ozsvath-Szabo 4-manifold invariants, Geom. Topol. 12 (2008), 1557-1651 (with S. Jabuka).
• On the Heegaard Floer homology of a surface times a circle, Adv. Math. 218 (2008), 728-761 (with S. Jabuka).

KEVIN McCRIMMON   [Home Page]
Professor; Ph.D., Yale University, 1965. Nonassociative algebras.

• A Taste of Jordan Algebras (550 pages), Springer-Verlag Universitext, Berlin, 2004.
• The splittest Kac superalgebra K₁₀ Journal of Algebra 313 (2007), 554-589.

TAI MELCHER   [Home Page]
Assistant Professor; Ph.D., University of California-San Diego, 2004. Stochastic analysis, geometry, and PDEs.

• Hypoelliptic heat kernel inequalities on the Heisenberg group, J. Functional Analysis 221(2) (2005), pp. 340-365 (with Bruce Driver).
• Malliavin calculus for Lie group-valued Wiener functions (submitted),
  arXiv:math.PR/0508419

BRIAN PARSHALL   [Home Page]
Gordon T. Whyburn Professor of Mathematics; Ph.D., Yale University, 1971. Representation theory.

• Reduced standard modules and cohomology, Transactions of the American Mathematical Society, to appear 2008 (with E. Cline and L. Scott).
• Quantum Groups and Finite Dimensional Algebras, Mathematical Surveys and Monographs, American Mathematical Society, vol. 150, 2008 (with B. Deng, J. Du, and J.-P. Wang).

KAREN V. H. PARSHALL   [Home Page]
Professor; Ph.D., University of Chicago, 1982. History of mathematics.

• James Joseph Sylvester: Jewish Mathematician in a Victorian World, Baltimore: Johns Hopkins University Press, 2006.
• Episodes in the History of Modern Algebra 1800-1950, HMATH, vol. 32, Providence: American Mathematical Society and London: London Mathematical Society, 2008 (co-edited with Jeremy J. Gray).

DONALD E. RAMIREZ   [Home Page]
Professor; Ph.D., Tulane University, 1966. Harmonic analysis and statistics.

• Anomalies in the Foundations of Ridge Regression, International Statistical Review, 76, 89-105 (2008) (with D. Jensen)
  http://arxiv.org/abs/math.ST/0703551
• Anomalies in the Analysis of Calibrated Data, Journal of Statistical Computation and Simulation 79(3)(2009), 299-314 (with D. Jensen).
  http://arxiv.org/abs/math.ST/0703550

ANDREI RAPINCHUK   [Home Page]
Professor; Ph.D., Institute of Mathematics, Academy of Sciences of Belarus, 1982. Group theory and number theory.

• Valuation-like maps and the congruence subgroup property, Invent. math. 144(2001), 571-607 (with Y. Segev).
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable, J. Amer. Math. Soc. 15 (2002), 929-978 (with Y. Segev and G. Seitz).

LEONARD L. SCOTT   [Home Page]
McConnell/Bernard Professor of Mathematics; Ph.D., Yale University, 1968. Group theory and representation theory.

• Semistandard filtrations in highest weight categories, Michigan Math. J. 58 (2009), 339-360.
• Reduced standard modules and cohomology, Trans. Amer. Math. Soc. 361 (2009), 5223-5261 (with Edward T. Cline and Brian J. Parshall).

DAVID E. SHERMAN   [Home Page]
Assistant Professor; Ph.D., University of California-Los Angeles, 2001. Operator algebras.

• Noncommutative L^p structure encodes exactly Jordan structure, Journal of Functional Analysis 221 (2005), 150-166.
• Unitary orbits of normal operators in von Neumann algebras, Journal für die Reine und Angewandte Mathematik 605 (2007), 95-132.

LAWRENCE E. THOMAS   [Home Page]
Professor; Ph.D., Yale University, 1970. Mathematical physics.

• Asymptotic behavior of thermal non-equilibrium steady states for a driven chain of anharmonic oscillators, Comm. Math. Phys. 215 (2000), 1-24 (with Luc Rey-Bellet).
  arXiv:math-ph/0001016
  
• Exponential convergence to non-equilibrium stationary states in classical statistical mechanics, Comm. Math. Phys. 225 (2002), 305-329 (with Luc Rey-Bellet).
  arXiv:math-ph/0110024

ROBERTO TRIGGIANI   [Home Page]
Professor; Ph.D., University of Minnesota, Minneapolis, 1973. Control theory for partial differential equations, applied mathematics.

• Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vols. 1 and 2 (with I. Lasiecka), Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1,067 pp., January 2000. Volume 3 in preparation.
• Carleman estimates with no lower-order terms for general Riemannian wave equations. Global uniqueness and observability in one shot, Applied Mathematics and Optimization, Special Issue in memory of J. L. Lions (2002) 331-375 (with P. F. Yao).
  

WEIQIANG WANG   [Home Page]
Professor; Ph.D., Massachusetts Institute of Technology, 1995. Representation theory.

• Representations of Lie superalgebras in prime characteristic I, Proc. London Math. Soc. (2009) (with Lei Zhao).
  arXiv:0808.0046
• Modular representations and branching rules for wreath Hecke algebras, IMRN (2008), Article ID: rnn128\-31 (with Jinkui Wan).
  arXiv:0806.0196