[ Français ]

There has always been a close and extremely fruitful interaction between Lie theory and mathematical physics --- an old example is Gell-Mann's flavour symmetry using the representation theory of the Lie algebra su_3. But this interaction has clearly deepened and blossomed significantly with the arrival of string theory. Consider for example all of the riches of the Wess-Zumino-Witten models which brought loop groups and affine algebras into the stringy fold, and all of the connections of Borcherd's theory of vertex operator algebras (an algebraicization of two-dimensional conformal field theory) with geometry, representation theory, subfactors, and number theory. The knot invariants of the 1980s are now understood in terms of topological quantum field theories, the structure of which has reached new levels recently with the work of Lurie and others. The list of Fields medalists since 1990 (e.g. the work of Witten, Jones, Drinfeld, Borcherds, Kontsevich, Werner, Smirnov all have overlap with the theory) emphasize the significance of strings/conformal field theory to pure mathematics. Lie theory in particular has been transformed forever and profoundly by string theory and related areas; conversely, string theory without Lie theory would be a race car without a motor. This interaction is showing absolutely no signs of slowing down. In light of these recent developments, it is an exciting time for a conference to bring together Lie theorists and mathematical physicists, in the expectation that further dialogue will stimulate additional interesting and important breakthroughs in both domains.