## Yifeng Yu : Random Homogenization of Non-Convex Hamilton-Jacobi Equations in 1d

- Applied Math and Analysis ( 97 Views )I will present the proof of the random homogenization of general coercive Hamiltonian in 1d with the form as H(p,x,\omega)=H(p)+V(x, \omega). Some interesting and complex phenomena associated with non-convex Hamiltonian will also be discussed. This is a joint work with Scott Armstrong and Hung Tran.

## Shahed Sharif : Who wants to be a millionaire?

- Applied Math and Analysis ( 90 Views )The Mordell-Weil theorem shows that the rational points on an elliptic curve defined over the field of rational numbers is a finitely generated abelian group. The Birch and Swinnerton-Dyer conjecture relates the rank of this group to a number of analytic and algebraic invariants of the curve. (More generally it considers an elliptic curve defined over a number field.) The conjecture is one of the Millennium Prize problems and the Clay Institute is offering a reward of 1 million dollars for a solution. This talk will be an introduction to the conjecture. In following weeks we will have lectures explaining each of the terms in the formula.

## Roger Temam : Mathematical Problems in Meteorology and Oceanography

- Applied Math and Analysis ( 22 Views )We will review the primitive equations of the atmoshere and the ocean and their coupling. We will descibe some mathematical poblems that they raise, some recent results and some less recent ones.