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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.
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A complete renormalization group trajectory between two fixed points, Comm. Math. Phys., to appear.
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]
Associate 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).
- Combinatorial characterizations of convexity and apartments in buildings, Australas. J. Combi. 34 (2006), 89-104 (with Hendrik Van Maldeghem).
GREGORY ARONE
[Home Page]
Associate Professor; Ph.D., Brown University, 1993.
Topology.
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Calculus of functors, operad formality, and rational
homology of embedding spaces, Acta Mathematica, to appear (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).
KAI-UWE BUX
[Home Page]
Assistant Professor;
Ph.D., J. W. Goethe-Universitaet, 1998.
Topology, algebra, and geometry (in particular, geometric group theory).
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The Bestvina-Brady construction revisited:
Geometric computation of Sigma-invariants for right-angled Artin groups,
J. London Math. Soc. (2) 60 (1999), no. 3, 793-801
(with C. Gonzalez).
- Finiteness properties of soluble arithmetic groups over global function fields, Geom. Top. 8 (2004), 611-644.
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 Lp, 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.
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Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED,
arXiv:math-ph/0702096 (with David Hasler).
arXiv:math-ph/0702096 -
Spiraling Attractors and Quantum Dynamics for a Class of Long Range Magnetic Fields, J. Functional Analysis, 24, 1-94 (2007) (with H. Cornean and E. Skibsted).
www.ma.texas.edu/mp_arc/ 02-452
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.
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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.
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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 -
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
SLAVA KRUSHKAL
[Home Page]
Associate Professor;
Ph.D.,
University of California-San Diego,
1996.
Low-dimensional topology and geometry.
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Exponential separation in 4-manifolds, Geom. Topol. 4 (2000) 397-405.
arXiv:math.GT/0008212 -
Subexponential groups in 4-manifold topology, Geom. Topol. 4
(2000), 407-430.
arXiv:math.GT/0001063
NICHOLAS J. KUHN
[Home Page]
Professor;
Ph.D.,
University of Chicago,
1980. Algebraic topology and representation theory.
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Tate cohomology and periodic localization of polynomial functors, Inventiones Mathematicae, 157 (2004).
arXiv:math.AT/0307173 - Generalized group characters and complex oriented cohomology theories, Journal A.M.S. 13 (2000), 553-594 (with M. J. Hopkins and D. C. Ravenel).
IRENA LASIECKA
[Home Page]
Professor;
Ph.D.,
University of Warsaw, Poland,
1975. Nonlinear partial differential equations,
mathematical control theory, applied mathematics.
- On nonlinear wave equations with degenerate damping and source terms, Trans. AMS 357 (2005), 2571-2611 (with V. Barbu and M. Rammaha).
- Mathematical Control Theory of Coupled PDE's, CBMS-NSF Conference Series in Applied Mathematics, SIAM, Philadelphia, 2002.
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).
- Schwarz-Pick type estimates, Complex Variables 48 (2003), 711-730 (with K. Stroethoff and R. Zhao).
THOMAS E. MARK
[Home Page]
Assistant Professor; Ph.D.,
Michigan State University,
2000.
Low-dimensional topology and geometry; gauge theory.
- Heegaard Floer homology of certain mapping tori II, in Geometry and Topology of Manifolds, Fields Institute Communications 47, H. Boden et. al., eds. Amer. Math. Soc. 2005 (with Stanislav Jabuka).
- Torsion, TQFT, and Seiberg-Witten invariants of three-manifolds, Geom. Topol. 6 (2002) 27-58.
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).
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Malliavin calculus for Lie group-valued Wiener functions (submitted),
arXiv:math.PR/0508419
IRINA MITREA
[Home Page]
Associate Professor;
Ph.D.,
University of Minnesota,
2000.
Harmonic analysis and partial differential equations.
- On the spectra of elastostatic and hydrostatic layer potentials on curvilinear polygons, J. Fourier Anal. Appl. 8(5) (2002), 443-487.
- Some Counterexamples for the Spectral Radius Conjecture, Diff. Int. Eqn. 16(12) (2003), 1409-1439 (with W. Tucker).
BRIAN PARSHALL
[Home Page]
Gordon T. Whyburn Professor of Mathematics;
Ph.D.,
Yale University,
1971. Representation theory.
- Linear quivers and the geometric setting for quantum GLn, Indag. Math. 13 (2003), 459-481 (with Jie Du).
- The restricted nullcone, Contemp. Math. 325 (2003), 51-75 (with J. Carlson, Z. Lin, and D. Nakano).
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.
- Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800-1945, Providence: American Mathematical Society and London: London Mathematical Society, 2002 (co-edited with Adrian C. Rice).
DONALD E. RAMIREZ
[Home Page]
Professor;
Ph.D.,
Tulane University,
1966.
Harmonic analysis and statistics.
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Anomalities in the Analysis of Calibrated Data,
(2007) (with D. R. Jensen).
http://arxiv.org/abs/math.ST/0703551v1 -
Computation of the generalized F distribution, Australian and New Zealand J. Statistics 43 (2001), 21-31 (with C. F. Dunkl).
http://arxiv.org/abs/math.ST/0703550v1
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.
- Some new examples in 1-cohomology, J. Algebra 260 (2003), 416-425.
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On Ext-transfer for algebraic groups, J. Transformation Groups, 9(3) (2004), 213-236 (with E. Cline and B. Parshall).
(Preprint on public site http://www.math.uga.edu/archive/.)
DAVID E. SHERMAN
[Home Page]
Assistant Professor;
Ph.D.,
University of California-Los Angeles,
2001. Operator algebras.
- Noncommutative Lp 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.
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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
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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.
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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.
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Spin Hecke algebras of finite and affine types,
Advances in Mathematics 212 (2007), 723-748.
- Integral operators and integral cohomology classes of Hilbert schemes, Math. Ann. 331 (2005), 669-692 (with Zhenbo Qin).
MathSciNet (mathematical reviews on the web)
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Algebraic and Geometric Topology
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Greg Arone | |
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Kai-Uwe Bux | |
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Slava Krushkal | |
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Nicholas Kuhn | |
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Thomas Mark |
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Analysis
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Tai Melcher | |
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Analytic Number Theory
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Jeffrey Holt | |
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Geometry
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Peter Abramenko | |
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Thomas Mark |
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Group Theory and Representation Theory
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Peter Abramenko | |
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Kai-Uwe Bux | |
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Mikhail Ershov | |
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Nicholas Kuhn | |
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Brian Parshall | |
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Andrei Rapinchuk | |
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Leonard Scott | |
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Weiqiang Wang | |
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Harmonic Analysis and Special Functions
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Donald Ramirez | |
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History of Mathematics
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Karen Parshall | |
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Mathematical Physics
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Abdelmalek Abdesselam | |
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Ira Herbst | |
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John Imbrie | |
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Lawrence Thomas | |
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Weiqiang Wang | |
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Mathematical Statistics
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Donald Ramirez | |
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Nonassociative Algebra
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Kevin McCrimmon | |
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Operator Theory, Function Theory, and Operator Algebras
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Thomas Kriete | |
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Barbara MacCluer | |
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David Sherman | |
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Applied Mathematics
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Christian Gromoll |
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Zoran Grujic | |
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Irena Lasiecka | |
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Irina Mitrea | |
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Roberto Triggiani | |
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Partial Differential Equations
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Zoran Grujic | |
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Irena Lasiecka | |
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Irina Mitrea | |
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Roberto Triggiani | |
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Probability
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Christian Gromoll |
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Tai Melcher | |
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