This talk is a survey on results concerning the Teichmuller space of negatively curved Riemannian metrics on M. It is defined as the quotient space of the space of all negatively curved Riemannian metrics on M modulo the space of all isotopies of M that are homotopic to the identity. This space was shown to have highly non-trivial homotopy when M is real hyperbolic by Tom Farrell and Pedro Ontaneda in 2009.

Title: Chang's Conjecture (joint with Monroe Eskew) Abstract: I will review some consistency results related to Chang's Conjecture (CC). First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems. Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously. We will aim to show the consistency of the statement: (\mu^+,\mu) -->> ( u^+,

Speaker: Zlil Sela
Title: Basic conjectures and preliminary results in non-commutative algebraic geometry

 Abstract: Algebraic geometry studies the structure of varieties over
 fields and commutative rings. Starting in the 1960's ring theorists
 (Cohn, Bergman and others) have tried to study the structure of varieties
 over some non-commutative rings (notably free associative algebras).

 The lack of unique factorization that they tackled and studied in detail,