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)
|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