Seminar 9 dec 97
V.M.Zakalyukin and Ricardo Uribe
The convex theorem of Darboux and aggregations in mathematical economics

Three different topics will be mentioned:

V.Zakalyukin

1. Aggregation problems in Mathematical economy and convex Darboux
   theorem.
   In a series of recent works of P.Chiappori and I.Ekeland
an active applications of Cartan exterior differential forms to
various problems of math. economy were started.
   One of them leads to the following question:
When a given 1-form on an affine space might be written as a
sum of differentials of convex functions multiplied by positive
functions (a convex analog of Darboux theorem)?

2. Simple classes of Lagrangian submanifold contact with coisotropic
subspace.
   This classification problem seems very natural  and  arises
in different settings, but was not solved yet.
   The list of these classes consists of A,B,C,D,E,F and one
exceptional class.

Ricardo Uribe ( Universite -Paris-7)

3. A version of Arnold minoration of vertices theorem for the curves in
hyperbolic spaces. An example of locally convex but not convex curve
in affine space.