11/19/2023 0 Comments Uiuc differential geometry![]() Mao Li, Higgs bundles, D-modules, and geometric Langlands conjecture.Sheldon Katz, Algebraic geometry, string theory.Jeremiah Heller, Motivic homotopy theory, algebraic cycles and K-theory.Haboush, Algebraic groups and homogeneous spaces. Iwan Duursma, Number theory, arithmetic geometry, coding theory and cryptography.Christopher Dodd, Algebraic and arithmetic geometry, D-modules, geometric representation theory.Steven Bradlow, Differential geometry, gauge theory, holomorphic vector bundles, moduli spaces.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. A major focus of the research of the algebraic geometry group is the exploration of these connections-and the discovery of exciting new ones. Algebraic geometry both contributes to and motivates these subjects, and makes use of developments in them. 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. 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. ![]() Algebraic geometry in simplest terms is the study of polynomial equations and the geometry of their solutions.
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