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.