Algebraic Geometry

Research Group

Introduction

The main interests of the algebraic geometry group are the followings: 1. Moduli theory: Moduli stacks of subschemes, vector bundles, sheaves, and objects in derived category. Gromov-Witten and Donaldson-Thomas theory, wallcrossing phenomena, derived algebraic geometry, Super geometry and quantum cohomology. 2. Birational geometry: Singularities, minimal model program 3. Topology of algebraic varieties: Hodge theory, algebraic cycles, motivic homotopy theory 4. Algebraic analysis: D-modules and perverse sheaves 5. Arithmetic geometry: Shimura varieties, Artin-Mazur formal groups 6. Application to physics: Topological string theory, Gauge theories, super Yang-Mills theory, Vafa-Witten and Kapustin-Witten theory, and Higgs bundles on algebraic curves and higher-dimensional varieties 7. Application to computer science: Commutative Algebra, Algebraic geometric implementation of codes, quantum codes