# Faculty Research - Pure Mathematics

- Algebra
- Number Theory and Algebraic Geometry
- Analysis
- Ergodic Theory and Dynamical Systems
- Geometry and Topology
- Logic
- Combinatorics

## Algebra

Paul Fong (Emeritus), Ph.D. Harvard University, 1959. Group theory; representation theory of finite groups.

Daniel Groves, Ph.D. University of Oxford, 2000. Geometric group theory.

Michael Hull, Ph.D. Vanderbilt University, 2013. Geometric group theory.

Nathan Jones, Ph.D. University of California - Los Angeles, 2005. Number Theory, Arithmetic Geometry.

Olga Kashcheyeva, Ph.D. University of Missouri, Columbia, 2003. Algebraic geometry and commutative algebra.

Richard G. Larson (Emeritus), Ph.D. University of Chicago, 1965. Applications of Hopf algebras to control theory and data mining; structure of Hopf algebras and quantum groups; applications of algebra to computer science.

Yanki Lekili, Ph.D. Massachusetts Institute of Technology, 2009. Symplectic Topology, Algebraic Geometry.

Jeffrey Leon (Emeritus), Ph.D. California Institute of Technology, 1971. Computation group theory; computational combinatorics.

John Lesieutre, Ph.D. Massachusetts Institute of Technology, 2014.

David E. Radford (Emeritus), Ph.D. University of North Carolina at Chapel Hill, 1970. Hopf algebras; quantum groups; invariants of knots, links and 3-manifolds.

Mark Ronan (Emeritus), Ph.D. University of Oregon, 1978. Groups; geometry.

Stephen Smith (Emeritus), Ph.D. Oxford University, 1973. Finite group theory; combinatorics; computer science; algebraic topology.

Bhama Srinivasan (Emeritus), Ph.D. University of Manchester, 1960. Representation theory of finite groups of Lie type .

Ramin Takloo-Bighash, Ph.D. Johns Hopkins University, 2001. Number Theory.

Kevin Tucker, Ph.D. University of Michigan, 2010. Algebraic Geometry and Commutative Algebra.

Matthew Woolf, Ph.D. Harvard University, 2014. Classical Algebraic Geometry, Derived Categories, Birational Geometry.

## Number Theory and Algebraic Geometry

Benjamin Antieau, Ph.D. University of Illinois at Chicago, 2010. Brauer groups, (derived) algebraic geometry, K-theory.

Alina Cojocaru, Ph.D. Queen's University, 2002. Number Theory
.

Izzet Coskun, Ph.D. Harvard University, 2004. Algebraic Geometry.

Lawrence Ein, Ph.D. University of California, Berkeley, 1981. Algebraic geometry.

Henri Gillet (Emeritus), Ph.D. Harvard University, 1978. Arithmetic geometry; algebraic geometry; algebraic k-theory.

Jack Huizenga, Ph.D. Harvard University, 2012. Algebraic Geometry.

Olga Kashcheyeva, Ph.D. University of Missouri, Columbia, 2003. Algebraic geometry and commutative algebra.

Anatoly S. Libgober (Emeritus), Ph.D. Tel-Aviv University, 1977. Topology of algebraic varieties; theory of singularities; mirror symmetry.

Ramin Takloo-Bighash, Ph.D. Johns Hopkins University, 2001. Number Theory.

Kevin Tucker, Ph.D. University of Michigan, 2010. Algebraic Geometry and Commutative Algebra.

Jan Verschelde, Ph.D. Katholieke Universiteit Leuven, Belgium, 1996. Computational algebraic geometry; symbolic-numeric computation; combinatorial and polyhedral methods; development of mathematical software; high performance computing; numerical analysis.

Stephen Yau (Emeritus), Ph.D. State University of New York-Stonybrook, 1976. Algebraic geometry, singularity theory; complex geometry; CR geometry; nonlinear filtering theory; algebraic geometry code; information theory; control theory; financial math; image database; computer software testing, Bioinformatics.

## Analysis

Neil Berger (Emeritus), Ph.D. Courant Institute of Mathematical Sciences, 1968. Elasticity, fluid mechanics.

Calixto Calderon (Emeritus), Ph.D. University of Buenos Aires, 1969. Harmonic analysis; differential equations; mathematical biology and history of science.

Alexey Cheskidov, Ph.D. Indiana University, 2004. Nonlinear PDE, fluid dynamics, and infinite-dimensional dynamical systems.

Mimi Dai, Ph.D. University of California - Santa Cruz, 2012. Partial differential equations, fluids dynamics, complex fluids.

David Dumas, Ph.D. Harvard University, 2004. Teichmuller theory, Kleinian groups, hyperbolic manifolds, geometric structures.

Shmuel Friedland, Ph.D. Technion - Israel Institute of Technology, 1971. Matrices, Tensors & Applications, Statistical Mechanics, Math. Biology, Dynamical Systems.

Michael Greenblatt, Ph.D. Princeton University, 1998. Resolution of singularities in analysis, oscillatory integrals, Radon transforms.

Jeff E. Lewis (Emeritus), Ph.D. Rice University, 1966. Analysis: Harmonic Analysis and Partial Differential Equations.

Charles S.C. Lin (Emeritus), Ph.D. University of California-Berkeley, 1967. Operator theory; perturbation theory; functional analysis.

Irina Nenciu, Ph.D. California Institute of Technology, 2005. Integrable systems, random matrices and mathematical physics.

Cheng Ouyang, Ph.D. Northwestern University, 2009. Probability theory and Stochastic analysis: diffusions and differential geometry, rough paths theory, Malliavin calculus and Gaussian processes, Levy processes.

Christian Rosendal, Ph.D. University of Paris 6, 2003. Descriptive set theory and applications.

Yoram Sagher (Emeritus), Ph.D. University of Chicago, 1967. Harmonic analysis, interpolation theory, mathematics education.

Andy Sanders, Ph.D. University of Maryland - College Park, 2013. Teichmuller theory, minimal surfaces, Kleinian groups, Higgs bundles and the geometry of character varieties.

Roman Shvydkoy, Ph.D. University of Missouri, Columbia, 2001. Euler, Navier-Stokes equations, turbulence, spectral problems, stability.

Zbigniew Slodkowski (Emeritus), Ph.D. Institute of Mathematics of the Polish Academy of Sciences, 1974. Several complex variables.

Christof Sparber, Ph.D. University of Vienna, 2004. Mathematical Physics, Partial Differential Equations, Analysis and Numerical Simulation of Multi-scale Problems.

David Tartakoff (Emeritus), Ph.D. University of California-Berkeley, 1969. Partial differential equations, several complex variables.

Zhihui Xie, Ph.D. The University of Texas at Austin, 2014. Math Physics, PDE, Harmonic Analysis.

Jie Yang, Ph.D. University of Chicago, 2006. Multiple comparisons, Cluster Analysis, Discriminant Analysis, Dimension Reduction, Design of Experiments, and Financial Mathematics.

## Ergodic Theory and Dynamical Systems

Shmuel Friedland, Ph.D. Technion - Israel Institute of Technology, 1971. Matrices, Tensors & Applications, Statistical Mechanics, Math. Biology, Dynamical Systems.

Alexander Furman, Ph.D. The Hebrew University of Jerusalem, 1996. Ergodic theory and Lie groups, especially aspects of rigidity for group actions.

Steven Hurder (Emeritus), Ph.D. University of Illinois-Urbana Champaign, 1980. Differential topology and geometry of foliations; smooth ergodic theory and rigidity of group actions; spectral and index theory of operators.

Howard A. Masur (Emeritus), Ph.D. University of Minnesota, 1974. Dynamical systems; low dimensional topology; Riemann surface theory.

## Geometry and Topology

Benjamin Antieau, Ph.D. University of Illinois at Chicago, 2010. Brauer groups, (derived) algebraic geometry, K-theory.

Aldridge K. Bousfield (Emeritus), Ph.D. Massacusetts Institute of Technology, 1966. Algebraic topology, homotopy theory.

Marc Culler (Emeritus), Ph.D. University of California, Berkeley, 1978. Group theory; low-dimensional topology; 3-manifolds; hyperbolic geometry; computation in geometry and topology.

David Dumas, Ph.D. Harvard University, 2004. Teichmuller theory, Kleinian groups, hyperbolic manifolds, geometric structures.

Brayton Gray (Emeritus), Ph.D. University of Chicago, 1965. Algebraic topology; homotopy theory.

Daniel Groves, Ph.D. University of Oxford, 2000. Geometric group theory.

James Heitsch (Emeritus), Ph.D. University of Chicago, 1971. Differential topology; theory of foliations; index theory; heat equation methods.

Jack Huizenga, Ph.D. Harvard University, 2012. Algebraic Geometry.

Michael Hull, Ph.D. Vanderbilt University, 2013. Geometric group theory.

Steven Hurder (Emeritus), Ph.D. University of Illinois-Urbana Champaign, 1980. Differential topology and geometry of foliations; smooth ergodic theory and rigidity of group actions; spectral and index theory of operators.

Louis Kauffman, Ph.D. Princeton University, 1972. Knot theory, topological quantum field theory, quantum topology, topological quantum computing and information.

Benjamin Klaff, Ph.D. Univeristy of Illinois at Chicago, 2003. low-dimensional topology, 3-manifolds, geometric group theory, informal STEM learning (math circles).

Yanki Lekili, Ph.D. Massachusetts Institute of Technology, 2009. Symplectic Topology, Algebraic Geometry.

Anatoly S. Libgober (Emeritus), Ph.D. Tel-Aviv University, 1977. Topology of algebraic varieties; theory of singularities; mirror symmetry.

Howard A. Masur (Emeritus), Ph.D. University of Minnesota, 1974. Dynamical systems; low dimensional topology; Riemann surface theory.

Andy Sanders, Ph.D. University of Maryland - College Park, 2013. Teichmuller theory, minimal surfaces, Kleinian groups, Higgs bundles and the geometry of character varieties.

Peter B. Shalen (Emeritus), Ph.D. Harvard University, 1972. Low-dimensional topology; geometric and combinatorial group theory; hyperbolic geometry.

Hyunshik Shin, Ph.D. Georgia Tech, 2014. Geometric group theory, Mapping class groups.

Brooke Shipley, Ph.D. Massachusetts Institute of Technology, 1995. Algebraic Topology and Homotopy Theory.

Kostyantyn Slutskyy, Ph.D. University of Illinois at Urbana-Champaign, 2012. Logic, Topology.

John Steenbergen, Ph.D. Duke University, 2013. Spectral Graph Theory, Simplicial Complexes, Dimension Reduction.

Andrew Suk, Ph.D. New York University, 2011. Discrete Geometry, Combinatorics.

Martin Tangora (Emeritus), Ph.D. Northwestern University, 1966. Algebraic topology.

Kevin Whyte, Ph.D. University of Chicago, 1998. Topology and geometric group theory .

John Wood (Emeritus), Ph.D. University of California, Berkeley, 1968. Differential and algebraic topology; topology of nonsingular varieties.

## Logic

John Baldwin (Emeritus), Ph.D. Simon Fraser University, 1971. Model theory: stability theory; applications to algebra and universal algebra; finite model theory; random graphs; math education.

Joel Berman (Emeritus), Ph.D. University of Washington, 1970. Universal algebra; ordered sets.

Fred Drueck, Ph.D. University of Illinois at Chicago, 2012. Logic, Practical Computer Programming.

Isaac Goldbring, Ph.D. University of Illinois at Urbana-Champaign, 2009. Model Theory, applications of nonstandard analysis to Lie Theory and Group Theory, Model Theory for Metric Structures, Operator Algebras.

William Howard (Emeritus), Ph.D. University of Chicago, 1956. Proof theory; foundations of mathematics; history of mathematics.

David E. Marker, Ph.D. Yale University, 1983. Mathematical logic; model theory; applications to algebra and geometry, real and complex exponetntation, connections between model theory and
differential algebra,
connections between model theory and descriptive set theory.

Christian Rosendal, Ph.D. University of Paris 6, 2003. Descriptive set theory and applications.

Dima Sinapova, Ph.D. University of California, Los Angeles, 2008. Logic and Set Theory. Large cardinals, forcing, infinitay combinatorics, cardinal arithmetic.

Kostyantyn Slutskyy, Ph.D. University of Illinois at Urbana-Champaign, 2012. Logic, Topology.

## Combinatorics

John Lenz, Ph.D. Univeristy of Illinois at Urbana-Champaign, 2011. Combinatorics, Theoretical Computer Science.

Dhruv Mubayi, Ph.D. University of Illinois at Urbana-Champaign, 1998. extremal and probabilistic combinatorics.

Vera Pless (Emeritus), Ph.D. Northwestern University, 1957. Coding theory; combinatorics.

Gyorgy Turan, Ph.D. Joszef Attila University, Hungary, 1981. Complexity theory; computational learning theory; combinatorics; logic.