Talk 1. Ritvik Ramkumar, Pure Mathematics Department, University of Waterloo
“Divisors on complex projective manifolds”
Ehsaan in his most recent talk, showed that on a smooth projective algebraic curve the divisor class group is isomorphic to the Picard group. In this talk, we generalize this results to the case of projective manifolds over C. In particular, if X is a complex projective manifold then Div(X) ∼= Pic(X). This will require results such as Bertini’s Theorem and Serre Vanishing, whose proofs will be sketched. Time permitting, we will discuss the scheme theoretic analogue of the above result.
Talk 2. Mohamed El Alami, Pure Mathematics Department, University of Waterloo
“First-order deformations II”
In this talk, we will take a purely algebraic approach to describe deformations of rings, algebraic varieties and schemes, and we will see how they relate to each other. We will then focus on the case of first-order deformations in order to classify them in some specific cases.