Dr Nivedita Viswanathan - Higher Fano Manifolds

Fano manifolds are manifolds whose first chern class is positive.  These are the building blocks in birational geometry and are known to have several nice properties, such as being covered by rational curves. That is, given a point on a Fano manifold, we can always find a rational curve through the point.  But when can we say that given a point, there is always a rational surface containing the point? What about being covered by 3-folds? And so on. In an attempt to answer these questions, I will address Fano manifolds with positive higher chern character. I will explicitly explain how we found some new examples of Fano manifolds that have positive second and third chern characters and what sort of an implication this has on the geometry of these varieties. This is joint work with Carolina Araujo, Roya Beheshti, Ana-Maria Castravet, Kelly Jabbusch, Svetlana Makarova, Enrica Mazzon and Libby Taylor.