Vishal Arul (MIT)

"Algebraic de Rham cohomology and the Gauss-Manin connection"

We will first define algebraic de Rham cohomology and show it agrees with classical de Rham cohomology for smooth projective complex varieties. Next, we will define connections and use a certain spectral sequence to construct the Gauss-Manin connection for the relative de Rham cohomology sheaves. Finally, we will interpret the horizontal sections for this connection as the ones arising from relative Betti cohomology.