Department of Mathematics, University of Utah

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801-581-6851, 801-581-4148 (fax)

Math Department Faculty, 1998--1999

This is a list of faculty available as thesis advisors for graduate students. For a more detailed list of Math Department personnel, consult our graduate bulletin.

DISTINGUISHED PROFESSORS

Fife, Paul C.

New York University, 1959. Applied Mathematics, Partial Differential Equations

A phase-field model for diffusion-induced grain boundary motion (with J. Cahn and O. Penrose), Acta Materiallia 45(1997) 4397--4413.
Traveling waves in a convolution model for phase transitions (with P. Bates, X. Ren, X. Wang), Archive Rat. Mech. Anal. 138(1997) 105--136.
Solidification fronts and solute trapping in a binary alloy (with Ch. Charach), SIAM J. Appl Math., to appear (1998).

Kollár, János,

Brandeis University, 1984. Algebraic Geometry

Nonrational Hypersurfaces, Jour. AMS 8 (1995), 241--249.
Shafarevich maps and automorphic forms, Princeton Univ. Press, 1995.
Rational curves on algebraic varieties, Springer Verlag, 1996.

PROFESSORS

Alfeld, Peter W.

University of Dundee, 1977. Approximation theory

Dimension and Local Bases of Homogeneous Spline Spaces (with M. Neamtu and L. L. Schumaker), SIAM J. Mathematical Analysis 27 (5) 1482--1501, Sept. 1996.
Upper and Lower Bounds on the Dimension of Multivariate Spline Spaces, SIAM J. Numerical Analysis 32 (2) 571--588, April 1996.
Understanding Mathematics, a www based study guide for undergraduate students,

Bestvina, Mladen

University of Tennessee, 1984. Topology

A combination theorem for negatively curved groups (with M. Feighn), Jour. Diff. Geom. 35(1) (1992), 85--101.
Train-tracks and automorphisms of free groups (with M. Handel), Annals of Math. 135 (1002), 1--51.
The boundary for negatively curved groups (with G. Mess), JAMS 4(3) (1991), 469--481.

Brooks, Robert M.

Louisiana State University, 1963. Topological Algebras

Analytic structure in the spectrum of a natural system, Pac. J. Math. 49 (1973), 315--334.
On the spectrum of an inverse limit of holomorphic function algebras, Adv. in Math. 19 (1976), 238--244.
Analytic structure in the spectra of certain uF-algebras, Math. Annalen 240 (1979), 27--33.

Burgess, C. Edmund

University of Texas, 1951. Topology (1/3 time)

Wild double tangent ball embeddings of spheres in E3 (with L. D. Loveland), Topology and its Applications 15 (1983), 231--237.
Classification of surfaces, Amer. Math. Monthly 92 (1985), 349--354.
Continuous functions and connected graphs, Amer. Math. Monthly 97 (1990), 337--339.

Carlson, James A.

Princeton University, 1971. Algebraic Geometry

Complex Hyperbolic Structures for Moduli of Cubic Surfaces (with D. Allcock, and D. Toledo), C. R. Acad. Sci. Paris 326, Ser. I, (1998), 49--54.
Quadratic Presentations and Nilpotent Kähler Groups (with Domingo Toledo), Journal of Geometric Analysis 5 (1995), 364--377.
On Fundamental Groups of Class Seven Surfaces (with Domingo Toledo), Bull. London Math. Soc. 29 (1997), no. 1, 98--102.

Cherkaev, Andrej V.

Leningrad Polytechnical Inst., 1979. Applied Matheamtics.

Which elasticity tensors are realizable? (with G. W. Milton). J. of Eng. Mat. and Technology 117 (1995), 483--493.
Optimal distribution of multimaterial composites for tortioned beams (with T. Burns), Structural Optimization, 13(1) (1997), 1--4.
The cavity of the optimal shape under the shear stress. (with Y. Grabovsky, A. Movchan, S. Serkov). To appear in International Journal of Solids and Structures.

Clemens, C. Herbert

University of California, Berkeley, 1966. Algebraic Geometry

Scrapbook of Complex Curve Theory, Plenum Press, 1980.
Homological equivalence, modulo algebraic equivalence, is not finitely generated, Publ. I. H. E. S. 57 (1983), 231--250.
Curves on generic hypersurfaces, Ann. Scien. Ec. Norm. Sup. 19 (1986), 629--36.

Coles, William J.

Duke University, 1954. Ordinary Differential Equations

A non-linear oscillation theorem, Proceedings, International Conference on Differential Equations, University of Southern California, Academic Press (1975), 193--202.
Oscillation for self-adjoint second order matrix differential equations, Differential and Integral Equations 1(4) (1991), 195--204.
Some oscillation results for second order matrix differential equations, (with M. K. Kinyon), Rocky Mountain Jour. Math. 1, (1994), 19--36.

Ethier, Stewart N.

University of Wisconsin, 1975. Applied Probability

A gambling system and a Markov chain, Annals of Applied Probability 6 (1996), 1248--1259.
Coupling and ergodic theorems for Fleming--Viot processes (with T. G. Kurtz), Annals of Probability (to appear).
Analysis of the Belgian progression, submitted for publication.

Fogelson, Aaron L.

New York Univ., 1982. Computational Fluids, Mathematical Physiology

Continuum models of Platelet Aggregation: Formulation and Mechanical Properties, SIAM JAM 52 (1992), 1089--1110.
Platelet Dense Granule Centralization and the Persistence of ADP Secretion (with Nien-Tzu Wang), Amer. Jr. Physiology, (270) (Heart Circ. Physiol 39: H1131-H1140 [1996]).
Modeling Biofilm Processes Using the Immersed Boundary Method (with Robert Dillon, Lisa Fauci and Donald Gavaer), submitted for publication.

Folias, Efthymios S.

California Institute of Technology, 1963. Applied Mathematics

The 3D Stress Field in a Laminated Composite Plate with a Hole Based on an h-r Finite Element Method, (with Y. Choi) ASME, AMD 196 November (1995), 31--42.
On the Design of Pressurized Vessels Against Fracture, Special volumes on Fracture in honor of A. A. Griffith, edited by G. Cherepanov (to appear).
Global Solutions of a Free Boundary Value Problem in Penetration Mechanics, Engineering Mechanics Today II (1996), 409--415.

Gersten, Stephen M.

Cambridge University, England, 1965. Group Theory

Cohomological lower bounds for isoperimetric functions on groups (with D. Allcock), to appear in Topology 1998. Preprint available
A homological characterization of hyperbolic groups, preprint (submitted for publication), Univ. of Utah 1998. Preprint available. .
Presentation and distortion of area in finitely presented groups, GAFA, 6 (1996), 301--345.

Glaser, Leslie C.

University of Wisconsin, 1964. Geometric Topology

Geometric Topology (edited with T. B. Rushing), Proc. Geometric Topology Conference, Park City, Utah, February 1974, 438, Lectures in Mathematics, Springer-Verlag, New York (1975), 459.
On tame Cantor sets in spheres having the same projection in each direction, Pacific J. Math. 60 (1975), 87--102.
On mildly cellular pseudo cells, Geometric Topology (edited with T. B. Rushing), Lectures in Mathematics, Springer-Verlag, New York 438 (1975), 215--224.

Golden, Kenneth

New York University, 1984. Applied Math

Critical behavior of transport in lattice and continuum percolation models, Physical Review Letters 78 (1997), 3935--3938.
Inverse electromagnetic scattering models for sea ice, (with D. Borup, M. Cheney, E. Cherkaeva, M. S. Dawson, K. H. Ding, A. K. Fung, D. Isaacson, S. A. Johnson, A. K. Jordan, J. A. Kong, R. Kwok, S. V. Nghiem, R. G. Onstott, J. Sylvester, D. P. Winebrenner and I. H. H. Zabel) Submitted for a special issue of IEEE Transaction in Geoscience and Remote Sensing. (in process).
Mathematics of Multiscale Materials, (with G. R. Grimmett, R. D. James, G. W. Milton, and P. N. Sen) (Eds.), IMA Volumes in Mathematics and its Applications, 99 Springer-Verlag, (in press).

Gross, Fletcher I.

California Institute of Technology, 1964. Group Theory

On the uniqueness of wreath products, J. Algebra 147 (1992), 147--175.
Hall subgroups of order not divisible by 3, Rocky Mt. J. Math. 23 (1993), 569--591.
Odd order Hall subgroups of the classical linear groups, Math. Zeit. 220 (1995), 317--336.

Gustafson, Grant G.

Arizona State University, 1968. Ordinary Differential Equations

Projection methods for nonlinear nodal problems (with P. W. Bates), Rocky Mtn. J. Math. 7 (1977), 569--608.
Uniqueness for nth order de la Vallèe-Poussin boundary value problems (with H. Gingold), Applicable Anal. 20(3--4) (1985), 201--220.
Solutions Branching in Linear differential equations (with Jerry Ridenhour), JDE 101(2) (1993), 373--387.

Hecht, Henryk

Columbia University, 1974. Lie Groups

On the cohomological dimension of localization function (with D. Milicic), Proc. Amer. Math. Soc. 108 (1990), 249--254.
A comparison Theorem for n-homology (with J. L. Taylor), Compositio Mathematica 86 (1993), 189--207.
On Casselman's compatibility theorem for n-homology, in Reductive Lie Groups, Proceedings of Cordoba Conference, Birkhäuser (1997).

Horvàth Lajos

Szeged University, 1982. Probability, Statistics

An asymptotic theory for empirical reliability and concentration processes (with M. Csörgo and S. Csörgo), Springer-Verlag, New York (1986).
Weighted approximations in probability and statistics (with M. Csörgo), Wiley, New York (1993).
Limit theorems in change-point analysis (with M. Csörgo), Wiley, New York (1997).

Kapovich, Michael

Soviet Academy of Science, 1988. Geometry

Quasi-isometries preserve the geometric decomposition of Haken manifolds, (with B. Leeb) Inventiones Math, 128 F.2 (1997), 393--416.
On the deformation theory of representations of fundamental groups of hyperbolic 3-manifolds (with J. Millson), Topology, 35 N 4 (1996), 1085--1106.
On dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups, Ann. Acad. Sci. Fenn., 23 (1998) 83--100.

Keener, James P.

California Institute of Technology, 1972. Applied Mathematics

A delay equation representation of pulse circulation on a ring in excitable media (with M. Courtemanche and L. Glass), SIAM J. Appl. Math. 56 (1996), 119--142.
The effect of gap junctional distribution on defibrillation, Chaos 8 (1998), 175--187.
A numerical method for the solution of the bidomain equations in cardiac tissue, (with K. Bogar) Chaos 8 (1998), 234--241.

Korevaar, Nicholas J.

Stanford University, 1981. Diff. Geometry and Partial Differential Equations

The global structure of constant mean curvature surfaces (with Rob Kusner), Invent. Math. 114 (1993), 311--332.
Harmonic maps to non-locally compact spaces, (with R. M. Schön), Comm. Anal. Geom. 5(2) (1997), 333--387.
Refined asymptotics for constant scalar curvature metrics with isolated singularities (with R. Mazzco, F. Pacard, R. M. Schön), Invent. Math. (to appear).

Mason, J. David

University of California, Riverside, 1968. Probability

Small-scale reproducibility estimates: an example using rebreathing measurements (with R. L. Jensen et al.), J. Appl. % Physiology 68 (1990), 1717--1721.
Operator-limit distributions in probability theory (a book with Z. J. Jurek), Wiley and Sons, 1993.
Operator-self-similar stable processes (with M. Maejima), Stochastic Processes and their Applications 54 (1994), 139--163.

Milicic, Dragan

University of Zagreb, 1973. Lie Groups

Equivariant derived categories, Zuckerman functors and localization (with P. Pandzic) in Geometry and Representation Theory of Real and p-adic Lie Groups, J. Tirao, D. Vogan, J. A. Wolf, Editors, Progress in Mathematics, 158, Birkhäuser, Boston, (1997), 209--242.
On degeneration of the spectral sequence for the composition of Zuckerman functors (with P. Pandzic), Glasnik Matematicki 32(52), (1997), 179--199.
The composition series of modules induced from Whittaker modules (with W. Sörgel), Comment. Math. Helv. 72, (1997), 503--520.

Milton, Graeme

Cornell University, 1985. Applied Mathematics

Which elasticity tensors are realizable (with A. V. Cherkaev) ASME J. Eng. Mat. Tech. 117 (1995), 483--493. (Special invited paper to commemorate the diamond jubilee of the materials division of the ASME).
Composites: A myriad of microstructure independent relations, proceedings of the 19th International Congress of Theoretical and Applied Mechanics, ed.` by T. Tatsumi, E. Watanabe, and T. Kambe, (1997), 443--459.
Finite frequency range Kramers Kronig relations: Bounds on the dispersion (with D. J. Eyre and J. V. Mantese) Phys. Rev. Lett. 79, (1997), 3062--3064.

Othmer, Hans G.

University of Minnesota, 1969. Applied Mathematics

Resonance in excitable systems under step-function forcing. II. Subharmonic solutions and persistence, Physica D (1996), 75--110.
A discrete cell model with adaptive signaling for aggregation of Dictyostelium discoideum, Phil. Trans. Roy. Soc. (Lon.), 1997, B352, 1--28.
Aggregation, Blowup and Collapse: The ABC's of generalized taxis, SIAM J. Applied Math., 1997 (to appear).

Roberts, Paul C.

McGill University, 1974. Commutative Algebra, Algebraic Geometry

Multiplicities and Chern Classes in Local Algebra, Cambridge University Press (1998)
Intersection Theory and the Homological Conjectures and Commutative Algebra, Proceedings of the ICM, Kyoto (1990).
The positivity of intersection multiplicities and symbolic powers of prime ideals (with K. Kurano), to appear.

Rossi, Hugo

Massachusetts Institute of Technology, 1960. Complex Analysis

Unitary structures on cohomology (with C. Patton), TAMS 290 (1985).
LeBrun's nonrealizability theorem in higher dimensions, Duke Math. J. 52 (1985), 457--424.
Cohomology on complex homogeneous manifolds with compact subvarieties (with C. Patton), The Lefshetz Conference, Contemporary Mathematics 58, 199--212.

Rushing, T. Benny

University of Georgia, 1968. Topology

Hausdorff Dimension of Wild Fractals, Trans. Amer. Math. Society 334(2) (1992), 597--611.
A Cellular Wedge in R³ (with R. B. Sher), Proc. Amer. Math Society 113(3) (1991), 895--898.
Approximating Homotopy Equivalences by Disk Bundle Projections (joint with Luis Montejano), Glasnik Mat. 22(42) (1987), 481--496.

Savin, Gordan

Harvard, 1988. Automorphic Forms

K-types of minimal representations (p-adic case), Glasnik Matematicki 31(51) (1996), 93--99.
Exceptional Theta-correspondences I (with K. Magaard), Compositio Math. 107 (1997), 89--123.
The dual pair PGL_3 times G2 (with B. Gross), Canadian Math. Bull. 40 (1997), 376--384.

Schmitt, Klaus

University of Nebraska, 1967. Nonlinear Analysis, Differential Equations

Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems (with V. K. Le), Springer Series in Applied Math., vol. 123, (1997).
On Newmann problems for semilinear elliptic equations with critical nonlinearity: Existence and symmetry of multipeaked solutions (with S. Maier and Z. Wang), Comm. PDE 22: (1997), 1493--1527.
On boundary value problems for degenerate quasilinear elliptic equations and inequalities (with V. K. Le), J. Diff. Equations 145 (1998), 170--208.

Taylor, Joseph L.

Louisiana State University, 1964. Group Representations

Analytic localization of group representations (with Henryk Hecht), Advances in Math. 79(2) (1990).
A comparison theorem for n-homology (with Henryk Hecht), Compositio Math. 86 (1990).
A geometric formula for characters of semisimple groups (with Henryk Hecht), submitted to Canadian J. Math.

Toledo, Domingo

Cornell University, 1972. Algebraic Geometry, Differential Geometry

Projective varieties with non-residually finite fundamental group, Pub. Maths. IHES 77 (1993), 109--125.
Quadratic presentations and nilpotent Kähler groups (with J. Carlson), Jour. Geom. Analysis 5 (1995), 359--377.
Fundamental groups of compact Kähler manifolds (with J. Amoros, M. Burger, K. Corlette, D. Kotschick), Surveys and Monographs in Mathematics 44 (1996), AMS, Providence, R. I.

Treibergs, Andrejs E.

Stanford, 1980. Differential Geometry

Applications of Eigenvalue Techniques to Geometry (with P. Li). Contemporary Geometry: J. Q. Zhong Memorial Volume (H. Wu, ed.) Plenum (1991) 21--52.
A reverse isoperimetric inequality, stability and extremal theorems for plane curves with bounded curvature (with R. Howard), Rocky Mountain Journal 25 (1995), 653--684.
Harmonic maps from the complex plane into surfaces with nonpositive curvature (with Z. C. Han, L. F. Tam and T. Wan), Communications in Analysis and Geometry 3 (1995), 85--114.

Trombi, Peter C.

University of Illinois, 1970. Lie Groups

Harmonic analysis of c ^P (G:H) (1<= p<2) , J. Funct. Anal. 40 (1981), 84--125.
Invariant harmonic analysis on split rank one groups with applications, Pacific J. Math. 100 (1982), 80--103.
Uniform Asymptotics for Real Reductive Lie Groups, Pacific J. Math. 146 (1990), 131--199.

Tucker, Don H.

University of Texas, 1958. Differential Equations, Functional Analysis

Concerning Differential Type Operators: A Preliminary Report (with Dang Thi Minh Ha), Proceedings, International Conference on Analysis and Mechanics of Continuous Media, Ho Chi Minh City, 27--29 December, 1995.
A new vector product (with J. F. Gold). In Proceedings of The 10th National Conference on Undergraduate Research, 1996.
A soapbox for science. In The National Honors Report, XVII, 1996.

ASSOCIATE PROFESSORS

Adler, Frederick R.

Cornell University, 1991. Mathematical Ecology

Modeling the dynamics of life: Calculus and probability for life scientists, Brooks/Cole, Pacific Grove, (1998).
Epistat: A computer program for identifying and testing interactions between pairs of quantitative trait loci (with K. Chase, F. R. Adler, and K. G. Lark), Theoretical and Applied Genetics 94, (1997), 724--730.
Case studies in mathematical modeling: Ecology physiology and cell biology (with H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon) (eds.), Prentice Hall, Upper Saddle River, New Jersey, (1997).

Bertram, Aaron

UCLA, 1989. Algebraic Geometry

Quantum Schubert Calculus, Adv. Math. 128, No. 2, (1997) 289--305.
Stable pairs and log flips, AMS Proceedings of Symposia in Pure Math, Vol. 62.1, (1997), 185--201.
Quantum multiplication of Schur polynomials, (with I. Ciocan-Fontanine and W. Fulton), Report No. 19, (1996--1997), Institute Mittag-Leffler, 20 pages.

Khoshnevisan, Davar

University of California, Berkeley, 1989. Probability Theory and Mathematical Statistics

The distribution of bubbles of Brownian sheet, The Annals of Probability 23(2) (1995), 786--805.
Levy classes and self-normalization, Electronic Journal of Probability 1 Paper No. 1 (1995), 1--18.
On a problem of Erdös and Taylor (with T. M. Lewis and Z. Shi), The Annals of Probability 24(2) (1996), 761--787.

Kleiner, Bruce

University of California, Berkeley, 1990. Differential Geometry

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. C. R. Acad. Sci. Paris Ser. I Math. 324(6) (1997) 639--643.
Conjugacy and rigidity for manifolds with a parallel vector field (with C. Croke), J. Diff. Geom. 39no.3, (1994), 659--680.
An isoperimetric comparison theorem, Invent. Math. 108, (1992), 37--47.

Lewis, Mark A.

Oxford, 1990. Mathematical Biology

Modelling territoriality and wolf-deer interactions (with J. D. Murray) Nature 366 (1993), 738--740.
Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent ``waves'' of damage, Theoretical Population Biology 45 (1994), 277--312.
Ecological chaos in the wake of invasion (with J. A. Sherratt and A. L. Fowler) Proc. Nat. Acad. Sci. 92 (1995), 2524--2528.

Smale, Nathan

University of California, Berkeley, 1987. Differential Geometry

Generic regularity of homologically area minimizing hypersurfaces in eight dimensional manifolds, Communications in Analysis and Geometry 1(2) (1993), 217--228.
Singular homologically area minimizing surfaces of codimension one in Riemannian manifolds, I. H. E. S. preprint (1996), (to appear in Inventiones).
A construction of homologically area minimizing hypersurfaces with higher dimensional singular sets, I. H. E. S. preprint (1997).

Zhu, Jingyi

New York University, 1989. Computational Fluid Dynamics

The second-order projection method for the backward-facing step flow and its comparison with experiments, J. Comput. Phys. 117 (1995), 318--331.
An Efficient Boundary Integral Method for the Mullins-Sekerka Problem (with X. Chen and T. Y. Hou), J. Comput. Phys. 127 (1996), 246--267.
A numerical study of chemical front propagation in a Hele-Shaw flow under buoyancy effects, Physics of Fluids (submitted).

ASSISTANT PROFESSORS

Balk, Alexander M.

Moscow Institute of Physics and Technology, 1988. Nonlinear Phenomena

A Lagrangian for water waves, Phys. Fluids 8 (1996) 416--420.
The suppression of short waves by a train of long waves, J. Fluid Mech. 315 (1996), 139--150.
New conservation laws for the interaction of nonlinear waves, SIAM Review 39 (1997), 68--94.

McLaughlin, Richard M.

Princeton University, 1994. Turbulent Transport

The Effect of Mean Flows on Enhanced Diffusivity in Transport by Incompressible Periodic Velocity Fields (with Andrew J. Majda), Studies in Applied Mathematics 89 (1993), 245--279.
An Explicit Example with non-Gaussian Probability Distribution for Nontrivial Scalar Mean and Fluctuation (with Andrew J. Majda), Physics of Fluids 8 (1996), 536--547.
Scalar Intermittency and the Ground State of Periodic Schrödinger Equations (with J. C. Bronski), Physics of Fluids 9 (1997), 181--190.

Morelli, Robert

Harvard University, 1989. Combinatorics and Algebraic Geometry

Pick's Theorem and the Todd Class of a Toric Variety, Advances in Mathematics 100(2) (August 1993), 183--231.
The Birational Geometry of Toric Varieties (to appear).
Ehrhart Polynomials, Hopf Algebras, and Special Values of Partial Epstein Zeta Functions (in preparation).

Niziol, Wieslawa

Princeton University, 1991. Algebraic Geometry

Crystalline conjecture via K-theory, to appear in Ann. Scient. Ecole Norm. Sup.
On the image of p-adic regulators, Inv. Math. 127, (1997), 375--400.
Duality in a cohomology of crystalline local systems. Comp. Math. 109, (1997), 67--97.

RESEARCH FACULTY

Cherkaeva, Elena

Leningrad University, 1988. Applied Mathematics

Source optimization in the inverse geoelectrical problem (with A. C. Tripp), Inverse Problems in Geophysical Applications, eds. H. W. Engl, A. Louis, and W. Rundell, SIAM, Philadelphia, 1997, 240--256.
Optimal source control and resolution in nondestructive testing, J. Structural Optimization 13(1997), 1, 12--16.
Inverse conductivity problem for inaccurate measurements (with A. C. Tripp), Inverse Problems 12(1996), 869--883.

Horn, Roger

Stanford University, 1967. Matrix Analysis

Contragredient Equivalence: A Canonical Form and Some Applications (with Dennis Merino), Linear Algebra Appl. 214 (1995), 43--92.
Inequalities for Monotonic Arrangements of Eigenvalues (with B. E. Cain and L. Luoluo), Linear Algebra Appl. 222 (1995), 1--8.
Norm Bounds for Hadamard Products and an Arithmetic-Geometric Mean Inequality for Unitarily Invariant Norms, Linear Algebra Appl. 223/224 (1995), 355--361.
When Does A*A = B*B and Why Does One Want to Know? (with I. Olkin), Amer. Math. Monthly, June 1996.

Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 801-581-6851, 801-581-4148 (fax) [30-Oct-1998].