# 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

Danko Adrovic, Ph.D. University of Illinois at Chicago, 2012. Polyhedral methods in algebraic geometry; generalization of polyhedral homotopies via tropical algebraic geometry.

Ben Bakker, Ph.D. Princeton University, 2010. Algebraic Geometry.

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

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 and Difference 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.

Nicole Looper, Ph.D. Northwestern University, 2018. Arithmetic dynamics, arithmetic geometry.

Ronnie Nagloo, Ph.D. University of Leeds, 2014. Differential Algebra, Model Theory and Number Theory.

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.

## Number Theory and Algebraic Geometry

Ben Bakker, Ph.D. Princeton University, 2010. Algebraic Geometry.

Richard A. P. Birkett, Ph.D. University of Notre Dame, 2023. Algebraic Dynamics, Complex Dynamics.

Alina Carmen Cojocaru, Ph.D. Queen's University, 2002. Number Theory / Arithmetic Geometry
.

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.

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

Eric Jovinelly, Ph.D. University of Notre Dame, 2023. 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.

Shiji Lyu, Ph.D. Princeton University, 2023. Commutative Algebra and Algebraic Geometry.

Gwyneth Moreland, Ph.D. Harvard University, 2023.

Julius Ross, Ph.D. Imperial College, London, 2004. Complex Analysis; Pluripotential Theory; Complex Geometry; Stability in algebraic Geometry; Planar flows and free boundary problems; Positivity in algebraic geometry; Hodge-Riemann bilinear relations.

Frederick Saia, Ph.D. University of Georgia, 2023. number theory and arithmetic geometry.

Nolan Schock, Ph.D. University of Georgia, 2022. Algebraic geometry and tropical 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.

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.

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

## 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.

Benjamin Call, Ph.D. The Ohio State University, 2022. Ergodic Theory, Dynamical Systems, Thermodynamical Formalism.

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

David Dumas, Ph.D. Harvard University, 2004. Geometric structures on manifolds, moduli spaces, character varieties, mathematical visualization.

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. Harmonic analysis, including singular integrals, oscillatory integrals, and Radon transforms and related operators.

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, SPDEs.

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. Categorical Data Analysis, Experimental Design, Bioinformatics, Biostatistics, Dimension Reduction, and Financial Mathematics.

## Ergodic Theory and Dynamical Systems

Richard A. P. Birkett, Ph.D. University of Notre Dame, 2023. Algebraic Dynamics, Complex Dynamics.

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.

Osama Khalil, Ph.D. The Ohio State University, 2019. Homogeneous Dynamics, Teichmueller Dynamics.

Nicole Looper, Ph.D. Northwestern University, 2018. Arithmetic dynamics, arithmetic geometry.

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

## Geometry and Topology

Benjamin Call, Ph.D. The Ohio State University, 2022. Ergodic Theory, Dynamical Systems, Thermodynamical Formalism.

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. Geometric structures on manifolds, moduli spaces, character varieties, mathematical visualization.

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; non-commutative geometry; 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.

Christopher Mahadeo, Ph.D. University of Saskatchewan, 2023. Broad: Differential geometry, mathematical physics, algebraic geometry, algebraic topology, condensed matter physics
Specific: Higgs bundles, topological recursion, spectral curves, quantum curves, topological insulators, hyperbolic materials.

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

Julius Ross, Ph.D. Imperial College, London, 2004. Complex Analysis; Pluripotential Theory; Complex Geometry; Stability in algebraic Geometry; Planar flows and free boundary problems; Positivity in algebraic geometry; Hodge-Riemann bilinear relations.

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. .

Nolan Schock, Ph.D. University of Georgia, 2022. Algebraic geometry and tropical 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 .

## 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. Practical computer programming.
.

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

Matthew Harrison-Trainor, Ph.D. University of California, Berkeley, 2017. Logic and computability theory.

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

David E. Marker (Emeritus), 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.

Scott Mutchnik, Ph.D. University of California, Berkeley, 2023. Model Theory.

Ronnie Nagloo, Ph.D. University of Leeds, 2014. Differential Algebra, Model Theory and Number Theory.

## Combinatorics

Vishesh Jain, Ph.D. Massachusetts Institute of Technology, 2020. High dimensional probability, randomized algorithms, probabilistic combinatorics.

Marcus Michelen, Ph.D. University of Pennsylvania, 2019. Probability and Combinatorics.

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

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