Meeting Times - Tuesdays, 7pm Pacific Time
Deformation theory has it’s origins both in Complex Geometry and Algebraic Geometry. Seen in its current form through the works of Michael Artin, Kunihiko Kodaira, it tries to answer questions on how infinitesimal changes affect the global structure of an algebraic variety. These infinitesimal changes could be brought on for instance through changes in the complex structure on a projective variety, or could be more drastic as smoothing of singularities.
The idea of deformations have been crucial for understanding the local behavior of Moduli Spaces of various objects, through Bend and Break lemmas in birational geometry, as precursors to virtual classes in enumerative geometry and as arithmetic deformations of abelian schemes.
Main Motive - The first half of the reading group will focus on core aspects of deformation theory. The second half will focus on applications and things people want to see and talk about using deformation theory (below listed are some of my ideas and my biases)