Harvard Differential Geometry Seminar
Spring 2018
Organizers: T. Collins and S.-T. Yau
The seminar meets on Tuesdays from 4:00 to 5:15 in SC 507, except as noted below.
Schedule
January 30, 2018
Valentino Tosatti (Northwestern)
- Estimates for collapsing Calabi-Yau metrics
[abstract]
Consider a compact Calabi-Yau manifold with a holomorphic fibration onto a lower-dimensional space, and consider a family of Ricci-flat Kahler metrics on the total space whose Kahler class is degenerating to the pullback of a class from the base. In earlier work, I proved that the metric collapse, away from the singular fibers, to a limiting metric on the base, in the locally uniform topology (and smoothly if the fibers are tori). I will describe new estimates that prove a uniform Holder bound in general, and bounds for all derivatives when the smooth fibers are isomorphic to each other. Joint work with H.-J. Hein.
February 6, 2018
Linyuan Lu (South Carolina)
- Ricci-flat graphs with girth at least five
[abstract]
A graph is called Ricci-flat if its Ricci curvatures vanish on all edges. Here we use the definition of Ricci curvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. We classified all Ricci-flat connected graphs with girth at least five: they are the infinite path, cycle $C_n$ ($n\geq 6$), the dodecahedral graph, the Petersen graph, the half-dodecahedral graph, and the Triplex graph. We also construct many Ricci-flat graphs with girth $3$ or $4$ by using the root systems of simple Lie algebras. (Joint work with Shing-Tung Yau and Yong Lin)
February 13, 2018
TBA -
[abstract]
February 20, 2018
TBA
- TBA
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February 27, 2018
TBA
- TBA
[abstract]
March 6, 2018
TBA
- TBA
[abstract]
March 20, 2018
TBA
- TBA
[abstract]
March 27, 2018
TBA
- TBA
[abstract]
April 3, 2018
TBA
- TBA
[abstract]
April 10, 2018
TBA
- TBA
[abstract]
April 17, 2018
TBA
- TBA
[abstract]
April 24, 2018
TBA
- TBA
[abstract]
Schedule for past years:
Fall 2016,
Fall 2017