Operads and Universal Algebra
June 21 – June 15, 2010, Capital Normal University, Beijing, China
June 28 – July 9, 2010, Nankai University, Tianjin, China
Chair: Jean-Louis Loday (CNRS and University of Strasbourg, France, email@example.com).
Vice-chair: Chengming Bai (Nankai University, Tianjin, China, firstname.lastname@example.org).
Members: Marcelo Aguiar (Texas A&MUniversity, US, email@example.com), Yuqun Chen (South China Normal University, China, firstname.lastname@example.org), Pierre-Louis Curien (CNRS and University of Paris VII, France, email@example.com), Li Guo (Rutgers University at Newark, US, firstname.lastname@example.org), Maria Ronco (University of Valparaiso, Chile, maria.ronco @uv.cl), Jim Stasheff (University of Pennsylvania, US, email@example.com.
Chair: Molin Ge (Nankai University, China, firstname.lastname@example.org).
Members: Chengming Bai (Nankai University, China, email@example.com), Leonid A. Bokut (South China Normal University and Sobolev Institute of Mathematics, Russia, firstname.lastname@example.org), Yuqi Guo (Southwest University, China, email@example.com), Shanzhong Sun (Capital Normal University, China, firstname.lastname@example.org).
Summary: An operad is a device that describes algebraic structures of different varieties in various categories. Instead of studying elements in a particular kind of algebra, the theory of operads studies operations that one can perform on this algebra. Even though operads and universal algebra have similar origins and ideas, they have their own distinct methods and applications. There are recent interests to understand better the connection between these two important areas of mathematics. The theory of operads finds its roots in the fifties in the notions of ”analyzeurs” and topological prop. Then it was systematically used in algebraic topology in the sixties by the American school. In the nineties, there was a renaissance of the operad theory due to the influence of Kontsevich, Loday and others. Since then, the operad theory has proved fruitful in analysing the various types of algebras which appeared at the same period (pre-Lie algebra, Gerstenhaber algebra, Leibniz algebra, dendriform algebra) and the various “algebras up to homotopy”. Its scope touched not only universal algebra, algebraic topology, deformation theory, but also theoretical physics, noncommutative geometry, computer science, combinatorial algebra and vertex operator algebra. Even though the study of operads is relatively new in China, many Chinese researchers have applied universal algebra in their study and are interested in understanding better the close relationship between operads and universal algebra. We will hold a three-week program on operad theory, emphasizing the relationship with universal algebra. The first and second of the program will consist of mini-courses that prepare the graduate students and non-experts for the more specialized talks in the third week of the program. The overall goal of the program is to bring the participants to the forefront of the current research in these areas.