Algebraic Geometry

Algebraic Geometry is a new emphasis area within the department. Algebraic Geometry in simplest terms is the study of polynomial equations and the geometry of their solutions. It is an old subject with a rich classical history, while the modern theory is is built on a more technical but rich and beautiful foundation. The future looks very bright indeed with promising new directions for research being undertaken, many of which connect algebraic geometry to other areas of mathematics as well as to physics.

Graduate Courses

The document Graduate Studies in Algebraic Geometry outlines the general areas of Algebraic Geometry studied here and describes the advanced undergraduate and graduate courses that are under development or offered regularly.

Algebraic Geometry Conferences and Seminars

• Algebraic Geometry: this week, this month, this year.
• Workshop on Donaldson-Thomas Invariants, March 17-20, 2005, University of Illinois at Urbana-Champaign.

Faculty Members in Algebraic Geometry

• Steven Bradlow. Differential geometry, gauge theory, holomorphic vector bundles, moduli spaces.
• Iwan Duursma. Number theory, Arithmetic geometry, Coding Theory and Cryptography.
• Daniel R. Grayson. Algebraic K-theory, motivic cohomology, algebraic geometry, number theory, computational algebra.
• William J. Haboush. Algebraic groups and homogeneous spaces.
• Sheldon Katz. Algebraic geometry, string theory.
• Tom Nevins. Algebraic geometry, noncommutative algebra, integrable systems
• Hal Schenck. Commutative Algebra and Algebraic Geometry

Faculty Members in Related Areas

• Matthew Ando. Algebraic Topology.
• John D'Angelo. Several complex variables and complex geometry.
• Maarten Bergvelt. Representation theory of infinite dimensional Lie algebras, algebraic geometry, super geometry.
• Sankar Dutta. Commutative algebra.
• Robert M. Fossum. Commutative algebra, algebraic groups, invariant theory, computer vision.
• Rinat Kedem. Mathematical physics, representation theory of infinite dimensional Lie algebras, quantum groups, and vertex algebras, integrable models statistical mechanics and quantum field theory.
• Rob Leigh (Department of Physics). String theory, non-commutative geometry.
• Anton Malkin. Geometry and representation theory
• Bruce Reznick. Combinatorial methods in algebra, analysis, number theory, combinatorics, geometry.

Graduate Students in Algebraic Geometry

• Shivi Bansal
• John Estabrook
• Yong Fu
• Kevin Jones
• Younsoo Kim
• Joshua Mullet
• Akira Sano
• Mehmet Sahin
• Artan Sheshmani
• Michael Sommers
• Jinhyung To
• Bin Wang

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