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 in commutative algebra, which arose in the 1960s out of a (successful) attempt to connect the theory with deep questions in number theory.

In the subsequent decades, the theory has found many connections with other areas of mathematics and physics, most notably string theory, representation theory, algebraic topology, combinatorics, and logic. Algebraic geometry both contributes to and motivates these subjects, and makes use of developments in them. A major focus of the research of the algebraic geometry group is the exploration of these connections---and the discovery of exciting new ones.

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.

Postdocs

  • Mao Li, Higgs bundles, D-modules, and geometric Langlands conjecture.

Faculty Members in Related Areas

  • Matthew Ando, Algebraic topology.
  • 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

  • Nachiketa Adhikari
  • Fulton Jackson
  • Justin Kelm
  • Sungwoo Nam
  • Ciaran O’Neill

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)
  • Euijin Hong (2019)
  • Mee Seong Im (2014)
  • Mi Young Jang
  • Chunyi Li (2014)
  • Itziar Ochoa
  • Matej Penciak (2019)
  • Mehmet Sahin (2009)
  • Alexandra Seceleanu (2011)
  • Jianyun Shan (2014)
  • Shiyu Shen (2019)
  • Artan Sheshmani (2011)
  • Yun Shi (2019)
  • Hongfei Tian (2017)
  • Jinhyung To (2012)
  • Joshua Wen (2020)
  • Lutian Zhao (2021)

Faculty working in Algebraic Geometry