Topics in Geometry (514-2-91)
Instructors
Aaron Charles Naber
Meeting Info
Lunt Hall 103: Mon, Wed, Fri 3:00PM - 3:50PM
Overview of class
Title: Analysis on finite and infinite dimensional spaces
Main Topic:
Physics terminology: We'll construct nonperturbative \phi^4 field theory based on 2 and 3 dimensional manifolds.
Math terminology: we'll prove existence of certain (apriori singular) linear evolution equations and measures on some infinite dimensional spaces.
A classic result proved by Glimme/Jaffe, we will give a new proof which takes just a few pages. Much of the class will be background working up to understanding all the words used above and the classical tools needed: linear pde's on finite dimensional spaces, function spaces and elliptic regularity through besov, gaussian measures on finite and infinite dimensional Hilbert spaces, Hamiltonian quantization (differentiation), Lagrangian quantization (integration), field quantization, renormalization (a purely nonperturbative point of view), linear pde's on infinite dimensional spaces.
Secondary topic:
Anthony McCormick will lecture on the Ginsburg Landau pde, beginning with the basics and working up to some open problems in the field.
Possible other topics:
Time allowing, the second part of the course may include several other topics of a few lectures each, including: Man-Chun, uniformization in kahler geometry; Neumayer, Gromov's torus rigidity for nonnegative scalar curvature; Hupp, Simon's construction of minimal hyper surfaces with irregular singular sets.
Class Materials (Required)
No textbook required
Class Materials (Suggested)
No materials suggested