The course is provided for students to learn basic materials for their thesis
and it will cover three parallel problems of current research issues in
analysis.
Free Boundary Problems: Tuesday 9:30-10:20. 210 MLH.
We will go over the seminal work by Alt and Caffarelli:
Existence and regularity for a minimum problem with free
boundary.
J. Reine Angew. Math. 325 (1981), 105--144.
Related Papers:
1.Caffarelli, Luis A.(1-TX); Jerison, David(1-MIT); Kenig, Carlos E.(1-CHI)
Some new monotonicity theorems with
applications to free boundary problems.
Ann. of Math. (2)
155 (2002), no. 2, 369--404.
2. Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. Global energy minimizers for free
boundary problems and full regularity in three dimensions. Noncompact problems at the intersection
of geometry, analysis, and topology, 83--97, Contemp. Math., 350,
Amer. Math. Soc.,
3. A SINGULAR ENERGY
MINIMIZING FREE BOUNDARY
DANIELA DE SILVA, DAVID JERISON
Fully Nonlinear
Problems on Manifolds: Thursday 9:30-10:20. 210 MLH
We will start out with the notes by Guan: Topics in Geometric Fully Nonlinear Equations
Mathematical Finance:
Friday 3:30-4:20. 210 MLH
We will talk about modeling of financial derivatives and financial and credit risks.