1. Isometrical embeddings with positive Gauss curvature: proof of openess in the continuity 
   method [pp 171-175 of book "Isometric embedding of Riemannian manifolds in Euclidean spaces", 
   by Q. Han and J.-X. Hong, 2006]
   ---------- Jeonghun Lee (April 9)

2. The semigroup approach to first order quasilinear equations in several space variables. 
   [paper by M. Crandall, Israel J. Math.  12  (1972), 108--132]
   ---------- Teng Zhang (April 11)

2a. The above could be combined with the paper: J. Rauch "BV estimates fail for most quasilinear 
   hyperbolic systems in dimensions greater than one."  Comm. Math. Phys.  106  (1986),  no. 3

3. Bifurcation Theory [Chapter 3 of "Topics in Nonlinear Functional Analysis" by L. Nirenberg]
   This could be prepared by 2 people, covering: 
   (a) Morse theory, (b) theorems by Krasnosielski and Rabinovitz
   ---------- Lam King Yeung and Teng Wang (March 24, 26, 28)

4. Generalized Implicit Function Theorems [Chapter 6 of "Topics in Nonlinear Functional Analysis" 
   by L. Nirenberg] This is clearly for more than one seminar and more than one person 
   - details to be discussed
   ---------- Hao Jia and Xin Shen (April 28, 30)

5. Convex sets and their extreme points: the Krein-Millman theorem and applications 
   [from Chapter 13.2 and following chapters in book by Lax "Functional Analysis"]
   ---------- Haoran Chen (April 7)

6. Helmholtz decomposition and Stokes operator (with different boundary conditions)
   [look in the book by R. Temam "Navier-Stokes equations. Theory and numerical analysis"]
   ---------- Qiliang Wu (May 5 and maybe part of May 7)

7. Krein-Rutman theorem [book by Deimling "Nonlinear Functional Analysis" page 226 
   and following applications]
   ---------- Linlin Su (April 14)

8. Method of Leray-Schauder degree for finding traveling waves. 
   [paper by Berestycki and Larrouturou "A semi-linear elliptic equation in a strip arising 
   in a two-dimensional flame propagation model" J. reine angew. Math., 396 (1989), 14--40.]
   [anoter related paper by Berestycki, Larrouturou and Lions in  Arch. Rat. Mech. Anal., 1990]

9. An optimal matching problem [paper by I.Ekeland from ESAIM-Control, Optimization and Calculus 
   of Variations, 2005]  This should be combined with a general introduction to the mass transfer
   Monge-Kantorovich problem [book by Villani "Topics in Optimal Transportation"] and, 
   if possible, some explanation on the applications (economic theory of hedonic pricing 
   - check other papers by Ekeland)
   ---------- Grzegorz Klima (April 21)

10. Young measures: existence theorem and basic properties [Chapter 6 from 1997 book by Pedregal],
    some applications [convergence of viscosity solutions to a conservation law: example 1 
    on page 207 of Tartar's notes "Compensated compactness and applications to PDEs" 
    Pitman Research Notes 1979]
    ---------- Liping Li (April 16)