Northeastern University MTH G375 Topics in Topology: Operads Time: Mon-Th 3:00-4:30 p.m. Room: 509 Lake Hall Instructor: Sasha Voronov Topics: operads and their relation to loop spaces, conformal field theory and variations, such as CohFT, graph homology, and string topology. In this one-semester course, I plan to give an introduction to operad theory in relation to topology and recent developments in mathematics coming from quantum field theory (QFT). Examples of QFT's include conformal field theory (CFT), topological CFT, cohomological field theory (CohFT), string theory, and quantum gravity. The theory of operads is an area of algebraic topology, which proved to be useful in the study of loop spaces in the seventies and has been undergoing a period of renaissance since the 90s, mainly because of recent applications to homotopy structures in algebra and topology, deformation quantization, and theoretical physics. You can see some lectures of a similar course I gave at University of Minnesota posted at http://www.math.umn.edu/~voronov/8390/index.html The course at Northeastern is revised to include string topology and new applications to topology. Prerequisites: Some familiarity with complex algebraic curves (or Riemann surfaces) and basic homology theory will be helpful. No knowledge of physics or operads is required - all necessary notions will be introduced along the way. Outline of the course: Introduction to operads; operads related to moduli spaces of algebraic curves; cyclic and modular operads; PROP's and algebraic theories; the little disks operad; the Fulton-MacPherson compactification; algebras over operads; algebras related to moduli spaces; homotopy algebras, including A_infty-, L_infty-, and G_infty-algebras; deformation quantization; introduction to CFT's, modular functors, and other 2d QFT's, such as topological QFT's, CohFT, CFT's, and quantum gravity; graph homology; string topology.