RTGC Seminar: Ideals in derived algebra and boundary conditions in AKSZ-type field theories

Seminar | January 27 | 4-5:30 p.m. | 939 Evans Hall

 Theo Johnson-Freyd, Perimeter Institute

 Department of Mathematics

For each dg operad P, I will present a homotopically-coherent version of "P-ideal". This presentation extends without change to a many-to-many generalization of operads with tree-level compositions called "dioperads". Whereas operads describe algebras, dioperads describe bialgebras, and "P-ideals" for a dioperad P are simultaneously ideals and coideals. In the case where P describes Frobenius algberas, P-ideals show up in relative Poincare duality. In the case where P describes Lie bialgebras, P-ideals are related to coisotropic submanifolds of derived Poisson manifolds. Koszul duality and exact triangles will also appear in my talk.