Talk #1: (1:00pm-2:15pm)
Jing Xuan Chen
"Holomorphic bisectional curvature"
The bisectional curvature on a Kähler manifold (M,J) is defined as H(X,Y)=R(X,JX,JY,Y) for unit vectors X,Y. We will see what we can prove about a compact connected Kähler manifold if we assume that it has positive bisectional curvature.
Talk #2: (2:30pm-4:00pm)
Spiro Karigiannis
"The deTurck trick demystified"
The Ricci flow is not strictly parabolic due to diffeomorphism invariance. This makes it harder to prove short-time existence of the flow. I will explain the “deTurck trick” to break the diffeomorphism invariance (also called gauge-fixing). This produced a modified flow that is strictly parabolic. One then shows that a solution to the modified flow can be transformed into a solution of the original flow.
MC 5403