## Research Areas in the Department

- Algebra
**Research Faculty with Primary Interests in this Area**Jee Heub Koh Valery Lunts Noah Snyder Michael Larsen Ajay Ramadoss Matthias Strauch Matvei Libine The algebra group has interests in commutative and non-commutative algebra, algebraic geometry, algebraic groups, Lie algebras and representation theory, and algebraic number theory.

- Analysis
**Research Faculty with Primary Interests in this Area**Hari Bercovici Ciprian Demeter David Fisher The analysts in the Mathematics Department reflect interests in harmonic analysis, complex analysis, potential theory, geometric measure theory, functional analysis, and summability theory. Several members of this group engage in research that is closely related to other groups in the department, such as Complex Analysis, Geometry, PDE and Applied Mathematics.

- Complex Analysis
**Research Faculty with Primary Interests in this Area**Matt Bainbridge Norm Levenberg Sergey Pinchuk The complex variables group is relatively small, but very active with many visitors.

- Dynamical Systems and Ergodic Theory
**Research Faculty with Primary Interests in this Area**Matt Bainbridge Chris Connell David Fisher Marlies Gerber Kevin Pilgrim A diverse and energetic group of internationally recognized faculty at Indiana University pursues research in dynamical systems and ergodic theory. Many of these faculty have overlapping interests in geometry, complex analysis and/or probability. Areas of interest include complex dynamics and its generalizations, connections between hyperbolic geometry and conformal iteration, ergodic theory, hyperbolic and partially hyperbolic dynamics, geodesic flows including billiards and the Teichmuller flow, and dynamics and rigidity of large group actions.

- Geometry
**Research Faculty with Primary Interests in this Area**Matt Bainbridge Chris Connell David Fisher Marlies Gerber Ji-Ping Sha Bruce Solomon Matthias Weber Research interests include the interaction between curvature and topology, geometry of Lie group actions, analysis of geometric variational problems from PDE and geometric measure theory viewpoints (e.g. Einstein manifolds, minimal submanifolds, and the Laplacian), and smooth dynamics.

- Logic
**Research Faculty with Primary Interests in this Area**Larry Moss William Wheeler The logicians in the Mathematics Department are part of the Indiana University Program in Pure and Applied Logic. Matching the interdisciplinary nature of logic, the program involves faculty members in Cognitive Science, Computer Science, History and Philosophy of Science, Informatics, Mathematics, and Philosophy. Taken together, IU has an impressive collection of logicians, mainly working on applied areas of the subject.

- Mathematical Physics
**Research Faculty with Primary Interests in this Area**Shouhong Wang The mathematical physics group at Indiana University has a long and strong tradition. The interests of current mathematical physics group include 1) field theory for the four fundamental interactions, 2) theoretical cosmology and astrophysics, 3) statistical physics, and 4) classical and geophysical fluid dynamics. The main objectives of the study of the group is to derive experimentally verifiable laws of Nature based on a few fundamental mathematical principles, and to provide new insights to a number of challenging problems in theoretical physics. We focus on symbiotic interplay between modern physics and advanced mathematics.

- PDE, Applied Mathematics, and Computation
**Research Faculty with Primary Interests in this Area**Michael Jolly Nam Le Peter Sternberg Roger Temam Shouhong Wang Kevin Zumbrun The group in PDE, applied mathematics and computation is one of the strongest such groups in the country. Research covers a wide array of nonlinear phenomena and involves work ranging from pure analysis to scientific computation.

- Probability and Combinatorics
**Research Faculty with Primary Interests in this Area**Miahi Ciucu Elizabeth Housworth Russell Lyons Faculty in Probability and Combinatorics are interested in random walks, probability on graphs, statistical mechanics, relations to geometric group theory, ergodic theory, andanalysis, applications of probability to problems in physics and biology, and algebraic, extremal, probabilistic and topological combinatorics, with an emphasis on connections to other areas of mathematics. Their research is well known internationally, has produced many published papers, and has led to a highly acclaimed graduate textbook.

- Topology
**Research Faculty with Primary Interests in this Area**James Davis Paul Kirk Ayelet Lindenstrauss Charles Livingston Michael Mandell Kent Orr Dylan Thurston Vladimir Touraev There is a very active group with interests including Geometric Topology (eg. Classical Knot Theory, 4-Manifold Theory, Higher Dimensional Knot and Link Theory, and Surgery Theory) and Algebraic Topology (eg. K-theory and Transformation Groups).