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 CalabiYau manifolds over higher dimensional bases  Abstract
We consider degenerations of CalabiYau manifolds over higher
dimensional bases in general. We then shall present a result on the
equivalence of a uniform diameter bound as Ricciflat KählerEinstein
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 KodairaSaito vanishing, I will prove a Nadeltype vanishing theorem for multiplier subsheaves, generalizing a number of vanishing theorems in algebraic geometry. If time permits, I will present an application to a Fujitatype freeness result for the lowest term in the Hodge filtration.

2.30pm  3.30pm

Gábor Székelyhidi (Notre Dame)
The KählerRicci flow and optimal degenerations  Abstract
ChenSunWang showed that the KählerRicci 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 "mostdestabilizing". An application of this result is a general
convergence result for the KählerRicci flow on Fano manifolds
admitting a KählerRicci soliton, generalizing works of TianZhu and
TianZhangZhangZhu. This work is joint with Ruadhai Dervan.

4.00pm  5.00pm

Mattias Jonsson (University of Michigan)
A variational approach to the YauTianDonaldson conjecture  Abstract
The YauTianDonaldson conjecture, recently proved by ChenDonaldsonSun, and Tian, asserts that a Fano manifold X admits a KählerEinstein 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 nonArchimedean geometry, but not use the continuity method nor CheegerColdingTian theory.

Organizers:
Supported by the Northwestern University Department of Mathematics, and the NSF.