MTH G375: Lecture Outlines

04/15/04: String Topology. The cacti operad and the framed little disks operad. The use of cacti operad to define string topology operations.

04/12/04: String Topology. The cacti operad.

04/08/04: The homology of the framed little disks operad: conclusion.

04/05/04: The homology of the framed little disks operad: a BV-algebra is an algebra over the homology framed little disks operad.

03/29/04: The homology of the framed little disks operad: algebras over it are BV-algebras.

03/25/04: The little disks operad, the framed little disks operad and the recognition principle.

03/22/04: Koszul theory of operads, VII. The cohomology of an algebra over a quadratic operad. Loop spaces. The little disks operad. The recognition principle.

03/18/04: Koszul theory of operads, VI. Koszulness of the associative, commutative, and Lie operads. The acyclicity of the tree complexes (planar and abstract).

03/15/04: Koszul theory of operads, V. The homology of an algebra over a quadratic operad.

03/11/04: Koszul theory of operads, IV. The zeroth cohomology of the dg dual is the quadratic dual. The Koszul complex of a quadratic operad.

03/08/04: Koszul theory of operads, III. The cobar construction for operads and the dg dual (review).

02/26/04: Koszul theory of operads, II. The cobar construction for operads and the dg dual.

02/23/04: Koszul theory of operads, I. Quadratic operads and quadratic duals.

02/19/04: The A_infty operad.

02/16/04: No course meeting: Presidents Day.

02/12/04: The Poisson operad. A_infty-algebras.

02/09/04: Free operads. Operad ideals. Operads defined by generators and relations. The associative and Lie operads revisited.

02/05/04: Operads. Algebras over operads. Examples: the commutative, Lie, and associative operads.

02/02/04: The Lie bialgebra PROP. Remarks about L_\infty-algebras and L_\infty bialgebras.

01/29/04: The Lie algebra PROP and algebras over it.

01/26/04: CFTs and VOAs. Topological field theories and Frobenius algebras. The Lie algebra PROP (started).

01/15/04: The equivalence of the two definitions of a PROP. Conformal field theories.

01/12/04: Symmetric monoidal categories.

01/08/04: Course meetings will be in 509 Lake Hall at 3 p.m. Mondays and Thursdays from now on. PROPs: definition, examples (the endomorhism PROPs, the graph PROP, the Riemann surface PROP, the moduli space PROP), algebras over PROPs.

01/06/04: Introduction. Overview of operad theory and the course.