Geometry & Topology RTG
University of Notre Dame
Mini workshop on complex geometry
April 29, 2017
We will have a one day meeting focused on complex geometry on Saturday, April 29.
All talks will be held in room 258, Hurley Hall .
|11:00 -- 11:30
|| Coffee and refereshments
|11:30 -- 12:20
||Mihai Păun (UIC)
|| Algebraic fiber spaces and positivity of
higher direct images
We will present a few recent
results obtained in collaboration
with Bo Berndtsson and Xu Wang.
As an application, we will discuss a new proof of
an important result due to Viehweg-Zuo.
|12:20 -- 2:00
|| Lunch break
|2:00 -- 2:50
||John Lesieutre (UIC)
|| A variety with non-finitely generated automorphism group
I will explain the construction of a smooth, projective variety for which the group of automorphisms is countable but not finitely generated.
|3:10 -- 4:00
|| Jian Xiao (Northwestern)
|| Positivity in the inverse σk equation
We discuss some positivity results in the conjecture proposed by Lejmi and Szekelyhidi on finding effective necessary and sufficient conditions for solvability of the inverse σk equation.
|4:20 -- 5:10
|| Valentino Tosatti (Northwestern)
|| Collapsing hyperkahler manifolds
Consider a projective hyperkahler manifolds with a surjective holomorphic map (with a section) with connected fibers onto a lower-dimensional manifold. In the case the base must be half-dimensional projective space, and the generic fibers are holomorphic Lagrangian tori. I will explain how hyperkahler metrics on the total space with volume of the torus fibers shrinking to zero, collapse smoothly away from the singular fibers to a special Kahler metric on the base, whose metric completion equals the global collapsed Gromov-Hausdorff limit, which has a singular set of real Hausdorff codimension at least 2. The resulting picture is compatible with the Strominger-Yau-Zaslow mirror symmetry, and can be used to prove a conjecture of Kontsevich-Soibelman and Gross-Wilson for large complex structure limits which arise via hyperkahler rotation from this construction. This is joint work with Yuguang Zhang.
Financial support for current and recent graduate students can be requested on the registration page before April 15.
For a preferred hotel rate at the Ivy Court use group "ND Math", confirmation number 8413, before March 28.
Contact: Gabor Szekelyhidi.