Enumerative Geometry Through Sheaves
Offered By: Stony Brook Mathematics via YouTube
Course Description
Overview
Explore enumerative geometry and its applications in algebraic geometry through a comprehensive lecture by Michail Savvas from the University of Texas at Austin. Delve into the world of geometric object counting, focusing on the relationship between geometric spaces like curves and more abstract concepts such as sheaves. Examine how sheaves generalize vector bundles and encode equations. Learn about moduli spaces and their role in parametrizing objects of interest, as well as the process of obtaining numerical invariants through integration of cohomology classes. Discover how this approach can be extended to cases where conventional assumptions do not hold. Investigate an important physics-motivated application: the construction of new generalized Donaldson-Thomas invariants for enumerating sheaves on Calabi-Yau threefolds. Gain insights from joint works with Young-Hoon Kiem and Jun Li in this one-hour Stony Brook Mathematics Colloquium presentation.
Syllabus
Enumerative geometry through sheaves - Michail Savvas
Taught by
Stony Brook Mathematics
Related Courses
Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and BeyondIMSA via YouTube On the Spectral Problem of a Three Term Difference Operator
IMSA via YouTube Homological Mirror Symmetry - Counting Curves on Calabi-Yau Threefolds
IMSA via YouTube Universally Counting Curves in Calabi-Yau Threefolds
IMSA via YouTube Moments of Families of Elliptic Curves
Hausdorff Center for Mathematics via YouTube