This spring all seminars will be held
on Zoom. The Zoom link for the seminar is here,
Passcode: 174362
Organizers: Anna Marie Bohmann, Rares Rasdeaconu, Ioana
Suvaina
Speaker:
Mitchell Faulk (Vanderbilt University)
Speaker:
Mitchell Faulk (Vanderbilt University)
Speaker:
Rares Rasdeaconu & Mitchell Faulk
(Vanderbilt University)
Speaker:
Hans-Joachim Hein (University of Muenster, Germany)
Title: The renormalized volume of a 4-dimensional Ricci-flat ALE space
Abstract: I will briefly
review the convergence theory for non-collapsed Einstein
4-manifolds developed by
Anderson-Cheeger, Bando-Kasue-Nakajima and Tian around 1990.
This was the main precursor for the
more recent higher-dimensional theory of
Cheeger-Colding-Naber. However, several difficult problems
have remained open even in dimension 4. I will focus on the
structure of the possible bubbles and bubble
trees in the 4-dimensional theory. In particular, I will
review Kronheimer's classical work on gravitational
instantons and explain a recent result of Biquard-H concerning
the renormalized volume of a 4-dimensional
Ricci-flat ALE space.
Speaker:
Alexandra Otiman (University of Florence, Italy)
Title: Variational problems in conformal geometry
Abstract: We study the
Euler-Lagrange equation for several natural functionals
defined on a conformal class
of almost Hermitian metrics, whose expression involves the Lee
form of the metric. We show that
Gauduchon metrics are the unique extremal points of the
functional corresponding to the norm of the Lee
form's codifferential. Moreover, in the spirit of Gauduchon's
celebrated result, we prove that in any given
conformal class, there exists a unique (up to scalar
multiplications) metric with special properties. This is
joint work with Daniele Angella, Nicolina Istrati and
Nicoletta Tardini.
Speaker:
Cristiano Spotti (Aarhus University, Denmark)
Title: On relations between K-moduli and symplectic geometry
Abstract: How much moduli
spaces of certain polarized varieties know about the
symplectic geometry of the
underneath manifold? After giving a general overview, I will
discuss work-in-progress with T. Baier, G. Granja
and R. Sena-Dias where we investigate some relations between
the topology of the moduli spaces of certain
varieties, of the symplectomorphism group and of the space of
compatible integrable complex structures.
In particular, using results of J. Evans, we show that the
space of such complex structures for monotone del Pezzo
surfaces of degree four and five is weakly homotopically
contractible.
Speaker:
Jiyuan Han (Purdue University)
Title: Variational approach to generalized Kahler Ricci Soliton equations
Abstract: By using the
variational approach, we show that on a log Fano variety, the
existence of a generalized
Kahler Ricci soliton (e.g, Kahler Einstein, Kahler Ricci
soliton) is equivalent to a uniform stability condition
(G-uniform g-Ding stable). Under a similar framework, we
also show the algebraic uniqueness of Kahler Ricci flow
limits on a Fano manifold. This project is a joint work with
Chi Li.
Speaker:
Mehdi Lejmi (CUNY, Bronx Community College)
Title: Deformations and blow-ups of conformally Kahler Einstein-Maxwell metrics
Abstract: Conformally
Kahler Hermitian metrics of constant Riemannian scalar
curvature and J-invariant Ricci are
called conformally Kahler Einstein-Maxwell metrics. In this
talk, we discuss deformations and possible construction
of such metrics on blow-ups. This is a joint work in progress
with Abdellah Lahdili.
Speaker: TBA
Title: TBA
Abstract: TBA
Friday, Apr 30th
Speaker:
Gabor Szekelyhidi (University of Notre Dame)
Title: Calabi-Yau metrics on C^n
Abstract: Recently a new
family of Calabi-Yau metrics on C^n was constructed by Li,
Conlon-Rochon, and myself, with
cylindrical tangent cone at infinity. I will discuss the
existence and uniqueness of these metrics.