Benson Farb - Rigidity of moduli spaces and algebro-geometric constructions

February 5, 2024 - Princeton University
Algebraic geometry contains an abundance of miraculous constructions, from ``resolving the quartic'' to the 27 lines on a smooth cubic surface to the Jacobian of a genus g curve. In this talk I will explain some ways to systematize and formalize the idea that such constructions are special: conjecturally, they should be the only ones of their kind.
I will state a few of these (mostly open) conjectures, and describe some methods used to solve some of them (coming from e.g. topology, geometric group theory, complex geometry). These conjectures can be viewed as forms of rigidity (a la Mostow and Margulis) for various moduli spaces and maps between them. They can also be viewed as a call for a ``systematic search'' for miracles.
Much of this talk should be understandable to advanced undergraduates.