Organizers: Anna Marie Bohmann, Madeline Brandt, Rares Rasdeaconu, and Ioana Suvaina
Speaker:
Garrett Michael Brown (UC Berkeley)
Title: The sign of scalar curvature on Kaehler
blowups
Abstract: In Kaehler geometry
there is a compelling interaction between the curvature of
the metric and the underlying
algebro-geometric structure. One example is that
positivity of the scalar curvature forces the the Kodaira
dimension to
be negative. I will explain a recent resolution to the
question of whether positive scalar curvature is preserved
under
birational transformation of Kaehler surfaces, resulting
in a classification (Contact person: Rares Rasdeaconu).
Friday, October
4th
Speaker:
Sofia Martinez Alberga (Purdue
University)
Title: Modeling Equivariant Simplicial Sets with
Simplicial Coalgebras
Abstract: Given a commutative ring R,
a $\pi_1$-R-equivalence is a continuous map of spaces
inducing an isomorphism on
fundamental groups and an R-homology equivalence between
universal covers. When R is an algebraically closed field,
Raptis and Rivera described a full and faithful model for
the homotopy theory of spaces up to $\pi_1$-R-equivalence.
They did
this by means of simplicial coalgebras considered up to a
notion of weak equivalence created by a localized version
of the cobar
functor. In this article, we prove a G-equivariant analog
of this statement using generalizations of a celebrated
theorem of Elmendorf.
We also prove a more general result about modeling
$G$-simplicial sets considered under a linearized version
of quasi-categorical
equivalence in terms of simplicial coalgebras. (Contact person:
Hannah Housden)
Friday, October
25th
Speaker:
Yifan Chen (UC
Berkeley)
Title: More Complete Calabi-Yau Metrics of Calabi
Type
Abstract: We construct more
complete Calabi-Yau metrics asymptotic to Calabi ansatz.
They are the higher-dimensional analogues
of ALH* gravitational instantons in two dimensions. Our
work builds on and generalizes the results of Tian-Yau and
Hein-Sun-Viaclovski-Zhang,
creating Calabi-Yau metrics that are only polynomially
close to the model space. We also prove the uniqueness of
such metrics in a given
cohomology class with fixed asymptotic behavior. (Contact
person: Ioana Suvaina)
Friday, November
8th
Speaker:
Valentina Zapata Castro (University
of Virginia)
Title: TBA
Abstract: (Contact person:
Hannah Housden)