Spring 2021

**
****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.