Analytic Methods in Algebraic Geometry Day
Mathematics Department
Northwestern University
Saturday March 18, 2017
Lunt Hall 105
Local Map
All are invited to attend, there is no registration.
Preliminary Schedule
9.30am - 10.00am
|
Breakfast
|
10.00am - 11.00am
|
Shigeharu Takayama (University of Tokyo)
Moderate degenerations of Calabi-Yau manifolds over higher dimensional bases - Abstract
We consider degenerations of Calabi-Yau manifolds over higher
dimensional bases in general. We then shall present a result on the
equivalence of a uniform diameter bound as Ricci-flat Kähler-Einstein
manifolds and that the limit varieties have canonical singularities at
worst.
|
11.30am - 12.30pm
|
Lei Wu (Northwestern)
Multiplier subsheaves and Hodge modules - Abstract
I will define the notion of multiplier subsheaves for generically defined variations of Hodge structures on smooth complex varieties (and more precisely for Hodge modules). I will present both algebraic and analytic constructions, inspired by those for multiplier ideals. Using Kodaira-Saito vanishing, I will prove a Nadel-type vanishing theorem for multiplier subsheaves, generalizing a number of vanishing theorems in algebraic geometry. If time permits, I will present an application to a Fujita-type freeness result for the lowest term in the Hodge filtration.
|
2.30pm - 3.30pm
|
Gábor Székelyhidi (Notre Dame)
The Kähler-Ricci flow and optimal degenerations - Abstract
Chen-Sun-Wang showed that the Kähler-Ricci flow on a Fano
manifold gives rise to a certain algebraic degeneration of the
manifold. I will discuss in what sense this degeneration is optimal,
or "most-destabilizing". An application of this result is a general
convergence result for the Kähler-Ricci flow on Fano manifolds
admitting a Kähler-Ricci soliton, generalizing works of Tian-Zhu and
Tian-Zhang-Zhang-Zhu. This work is joint with Ruadhai Dervan.
|
4.00pm - 5.00pm
|
Mattias Jonsson (University of Michigan)
A variational approach to the Yau-Tian-Donaldson conjecture - Abstract
The Yau-Tian-Donaldson conjecture, recently proved by Chen-Donaldson-Sun, and Tian, asserts that a Fano manifold X admits a Kähler-Einstein metric if and only if X is K-(poly)stable. I will present joint work with Robert Berman and Sebastien Boucksom, on a new, variational, proof of this conjecture in the case X has no vector fields. Our proof uses pluripotential theory and ideas from non-Archimedean geometry, but not use the continuity method nor Cheeger-Colding-Tian theory.
|
Organizers:
Supported by the Northwestern University Department of Mathematics, and the NSF.