Explore a comprehensive lecture on Homological Mirror Symmetry and Categorical Donaldson-Thomas Theory delivered by Tudor Padurariu from Columbia University. Delve into the intricacies of Donaldson-Thomas invariants, their refinements, and categorifications, with a focus on the example of points on C^3. Discover the construction of categorical analogues of BPS invariants and their applications in categorical DT/Pandharipande-Thomas correspondence. Gain insights into vector spaces, dimensional reduction, categorization, numerical DP invariants, universe schemes, quasiBPS categories, and MDW key theory. Understand the technical challenges involved and the potential applications of this advanced mathematical concept in the field of algebraic geometry and string theory.
Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond
Overview
Syllabus
Introduction
Vector Spaces
Dimensional Reduction
Categorization
Categorical DT Theory
Numerical DP Invariant
Universe Scheme of D Points
Category of C3
DP Category
quasiBPS Categories
MDW
Key Theory
Applications
Technical difficulties
Taught by
IMSA
