# Faculty Research - Pure Mathematics

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

## Algebra

Martina Bode, Ph.D. Brandeis University, 1996. Math Education and
Director of the Chicago Symposium Series
.

Rankeya Datta, Ph.D. University of Michigan- Ann Arbor, 2018. Algebraic Geometry and Commutative Algebra.

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

James Freitag, Ph.D. University of Illinois at Chicago, 2012. Model Theory, Algebraic Differential Equations, Commutative Algebra and Algebraic Geometry, Number Theory, Machine Learning.

Daniel Groves, Ph.D. University of Oxford, 2000. 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.

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 .

Nicholas Switala, Ph.D. University of Minnesota, 2015. Commutative algebra, algebraic geometry.

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

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

Wenliang Zhang, Ph.D. University of Minnesota, 2008. Commutative Algebra, Algebraic Geometry.

## Number Theory and Algebraic Geometry

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

Alina Carmen 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.

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.

Howard Nuer, Ph.D. Rutgers University, 2016. Algebraic Geometry, Moduli of sheaves, Bridgeland stability, Derived Categories, Mirror Symmetry.

Julius Ross, Ph.D. Imperial College, London, 2004. Complex Analysis; Pluripotential Theory; Complex Geometry; Stability in algebraic Geometry; Planar flows and free boundary problems.

Nicholas Switala, Ph.D. University of Minnesota, 2015. Commutative algebra, algebraic geometry.

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 and Partial Differential Equations

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, hyperbolic geometry, geometric structures, and character varieties.

Shmuel Friedland (Emeritus), Ph.D. Technion - Israel Institute of Technology, 1971. Tensors & Applications, Matrices, Quantum Information , Math. Biology, Dynamical Systems.

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

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. Mathematical logic and applications.

Julius Ross, Ph.D. Imperial College, London, 2004. Complex Analysis; Pluripotential Theory; Complex Geometry; Stability in algebraic Geometry; Planar flows and free boundary problems.

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

Roman Shvydkoy, Ph.D. University of Missouri, Columbia, 2001. Collective dynamics, 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.

Jie Yang, Ph.D. University of Chicago, 2006. Big Data Analysis, Experimental Design, Bioinformatics, Biostatistics, Dimension Reduction, and Financial Mathematics.

## Ergodic Theory and Dynamical Systems

Shmuel Friedland (Emeritus), Ph.D. Technion - Israel Institute of Technology, 1971. Tensors & Applications, Matrices, Quantum Information , 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, hyperbolic geometry, geometric structures, and character varieties.

Eduard Einstein, Ph.D. Cornell University, 2018. Geometric Group Theory.

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.

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 (Emeritus), Ph.D. Princeton University, 1972. Knot theory, topological quantum field theory, quantum topology, topological quantum computing and information.

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.

Laura Schaposnik, Ph.D. University of Oxford, 2013. Geometric aspects of Higgs bundles and the Hitchin fibration, as well as mathematical physics, and differential and algebraic geometry. .

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

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

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

Wouter Van Limbeek, Ph.D. University of Chicago, 2015. Differential geometry,
Geometric structures on manifolds,
Geometric topology,
Discrete subgroups of Lie groups.

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. Mathematical logic and practical computer programming.
.

James Freitag, Ph.D. University of Illinois at Chicago, 2012. Model Theory, Algebraic Differential Equations, Commutative Algebra and Algebraic Geometry, Number Theory, Machine Learning.

Sherwood Hachtman, Ph.D. University of California, Angeles, 2015. logic, foundations, set theory, large cardinals.

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 exponentiation, connections between model theory and
differential algebra,
connections between model theory and descriptive set theory.

Christian Rosendal, Ph.D. University of Paris 6, 2003. Mathematical logic and applications.

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

## Combinatorics

Dhruv Mubayi, Ph.D. University of Illinois at Urbana-Champaign, 1998. Combinatorics.

Will Perkins, Ph.D. New York University, 2011. Probability, statistics, algorithms, and 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.