Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                                Spring 2021

Fridays, 12:10-1:00pm in SC 1320 (unless otherwise noted)

    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

                  Friday, Feb 12th, Kahler Geometry Workgroup - Discussion

Speaker:  Mitchell Faulk (Vanderbilt University)           

                  Friday, Feb 26th, Kahler Geometry Workgroup - Discussion

Speaker:  Mitchell Faulk (Vanderbilt University)

                  Friday, Mar 12th, Kahler Geometry Workgroup - Discussion

Speaker: Rares Rasdeaconu & Mitchell Faulk (Vanderbilt University) 

                  Friday, Mar 19th

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.

                 Friday, Mar 26th

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.

                  Friday, Apr 2nd

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.

                  Friday, Apr 9th

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.

                  Friday, Apr 16th (the talk will start at 12:30pm)

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.


                 Friday, Apr 23th

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.


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