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: A monoid can be interpreted as a category with a single object, where the morphisms correspond to the elements of the monoid.
Extending this concept to higher categories, in this talk I will explore the relationship between complete Segal spaces with a monoidal
structure and complete Segal Theta_2-spaces, considering an approach capturing the idea of having a single object that aligns with the
nature of the previously mentioned work. In this talk, I will not assume any prior knowledge on Segal or Theta_2 spaces.) 

Abstract:  (Contact person: Hannah Housden)