The first meeting will be in WEH 8201 on August 31.

Geometric Measure Theory is voted to be the topic this semester. We will meet every week on Thursday, 2:30-3:30 in WEH 7218.

We will most likely follow the lecture notes by Leon Simon, which is available here.

Another great resource is Frank Morgan’s book, which is freely available to CMU students via the library.

For the first part of the working group, good references are:

  • Evans & Gariepy’s “Measure theory and fine properties of functions”

  • Maggi’s “Sets of finite perimeter and geometric variational problems”. This is available via the library as well.

If you are bored about the pace of the working group, here’re some movies that could excite you.

Schedule (so far)

Name Chapter(s) Date Topic
    08/31 Introduction and scheduling
Adrian Hagerty   09/07 Hausdorff measure
Kerrek Stinson   09/14 Differentiation of Radon measure, approximate limits, densities
Giovanni Gravina   09/21 Lipschitz functions, area and coarea formulas, sets of finite perimeters
Sam Cohn   09/28 Differential forms
Kevin Ou   10/05 Rectifiable and Integral Currents, Boundary Operator, Pushforward of a Current, Currents representable by Integration
Antoine Remond-Tiedrez   10/12 Rectifiability of currents
Won Eui Hong   10/19, 10/26 Deformation and approximation Theorems, Isoperimetric Theorem for Currents
Son Van   11/02, 11/09 Slicing, Closure Theorem, Compactness Theorem, Existence of area-minimizing surfaces
Adrian Hagerty   11/16 Properties of area-minimizing currents

Participants (so far that is known to the organizers): Adrian Hagerty, Antoine Remond-Tiedrez, Son Van, Giovanni Gravina, Won Eui Hong, Kerrek Stinson, Sam Cohn, Likhit Ganedi, Yangxi (Kevin) Ou