Department of Mathematics and Statistics
                          The University at Albany
                                      
                                 COLLOQUIUM
                                      
                              Alberto De Sole
                                      
                             Harvard University
                                      
                      Classical and Quantum W Algebras
                                      
                          Friday, October 26, 2007
                                      
                             4:15 p.m., ES 143
                                      
                          Tea at 3:45 p.m., ES 152
                                      
                                  ABSTRACT
                                      
   I will first introduce the notions of vertex algebra and Poisson
   vertex algebra, and the relation between them via the so called quasi-
   classical limit. I will then introduce the Zhu algebra of a vertex
   algebra, which controls its representations, both in the quantum and
   in the classical case. As a special case, I will consider the affine
   and finite W algebras, obtained by the method of quantum Hamiltonian
   reduction.