Abstract: We’ll begin with complex differential geometry, focusing on a special class of complex manifolds called Kähler manifolds. We’ll then construct the Chern connection and discuss the first Chern class. We’ll introduce Hodge theory by developing Dolbeault cohomology and discuss the Hodge and Lefschetz decompositions for compact Kähler manifolds. Finally, we introduce Hodge structures and Hodge numbers and compute examples for weight 1 and 2 cases. This first talk will focus on the complex geometry.
