Algebraic Geometry

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 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.

Faculty Members in Algebraic Geometry

  • Steven Bradlow. Differential geometry, gauge theory, holomorphic vector bundles, moduli spaces.
  • Christopher Dodd. Algebraic and Arithmetic Geometry, D-modules, Geometric Representation Theory.
  • Iwan Duursma. Number theory, Arithmetic geometry, Coding Theory and Cryptography.
  • William J. Haboush. Algebraic groups and homogeneous spaces.
  • Jeremiah Heller. Motivic homotopy theory, algebraic cycles and K-theory.
  • Sheldon Katz. Algebraic geometry, string theory.
  • Tom Nevins. Algebraic geometry, geometric representation theory, mathematical physics.

Postdocs

  • Laura Escobar, Combinatorial aspects of algebra and algebraic geometry.
  • Cary Malkiewich. Algebraic Topology, specifically homotopy theory, smooth manifolds, and algebraic K-theory.
  • Rebecca Tramel, Algebraic geometry, derived categories, in particular Bridgeland stability conditions.

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.
  • 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.
  • James Pascaleff. Symplectic topology and mirror symmetry.
  • Bruce Reznick. Combinatorial methods in algebra, analysis, number theory, combinatorics, geometry.
  • Alexander Yong, Combinatorial aspects of algebra and geometry; algebraic combinatorics

Graduate Students in Algebraic Geometry

  • Euijin Hong
  • Mi Young Jang
  • Itziar Ochoa
  • Matej Penciak
  • Shiyu Shen
  • Yun Shi
  • Hongfei Tian
  • Joshua Wen

Recent Algebraic Geometry Alumni

  • Shivi Bansal (2008)
  • Jinwon Choi (2012)
  • Michael DiPasquale (2015)
  • Eliana Duarte (2017)
  • Abdulla Eid (2013)
  • Nathan Fieldsteel¬†(2017)
  • Yong Fu (2010)
  • Mee Seong Im (2014)
  • Chunyi Li (2014)
  • Mehmet Sahin (2009)
  • Alexandra Seceleanu (2011)
  • Jianyun Shan (2014)
  • Artan Sheshmani (2011)
  • Hongfei Tian (2014)
  • Jinhyung To (2012)