Jeffrey Case

PDL C401
Abstract: The Rumin and bigraded Rumin complexes are CR analogues of the De Rham and Dolbeault complexes, respectively. In the first part of this talk, I summarize some applications of Hodge theory for the De Rham and Dolbeault complexes to motivate the introduction of the (bigraded) Rumin complex. In the second part of this talk, I describe a new construction of the Rumin and bigraded Rumin complexes using differential forms which give them the structure of a Cinfinity algebra, as well as some applications. Of particular note is a nonlocal Hodge theorem which gives rise to a Hodge decomposition theorem for closed Sasakian manifolds which is analogous to the wellknown Hodge decomposition theorem for Kahler manifolds.