Fall 2019:

8/23: Prof. Luigi Vezzoni (U. di Torino)
Title:
Geometric flows of Balanced metrics
Note: Room 3309 for this meeting
Abstract:
An Hermitian metric g on a complex manifold (M, J) is called balanced if its
fundamental
form is coclosed. Typically examples of balanced manifolds are given by
modifications of Kahler
manifolds, twistor spaces over antiselfdual oriented Riemannian 4manifolds
and nilmanifolds. In the
talk it will be discussed two new geometric flows of balanced structures. The
first of them was introduced
in [1] and consists in a generalisation of the Calabi flow to the balanced
context. The flow preserves
the BottChern cohomology class of the initial structure and in the Kahler
case reduces to the classical
Calabi flow. The other flow still preserves the BottChern class of the
initial structure but, in contrast
with the first one, it is a potential flow and it does not preserve the
Kahler condition.
For the both flows it will be discussed the wellposedness and the stability
around KahlerEinstein
metrics.

8/30: Organizational meeting
Faculty and students welcome
Abstract: We will make a plan on topics to cover, as well as potential papers to read
and work through on days when no speakers are scheduled. Come with questions
and/or ideas.

9/6: Prof. Scott Wilson
Title: Harmonic symmetries for Hermitian manifolds
Abstract: I will report on some recent work that generalizes the symmetries of
the Hodge numbers of Kahler manifolds to the more general setting of compact
complex manifolds with compatible metric. I will review some introductory
material and the talk will be self contained. New attendees and students
are especially welcome. Here is a preprint:
arxiv:1906.02952.

9/13: Prof. Luis Fernandez (BCC CUNY)
Title: Basics on almost complex manifolds
Abstract:
Given that some of the regular attendees to the seminar will be away, I will
do a general review of basic facts about almost complex, complex, almost
Kahler, and Kahler manifolds, including metrics, connections, and questions
about integrability. I will look at some particular examples of these objects
in some detail (especially the 6 sphere).
The talk is intended for a general audience with some knowledge of (real)
differential geometry. Students are very welcome.

9/20: Santiago Simanca
Title: Elementary Almost Hermitian Properties of Products of Spheres
Abstract: We consider products of two odd dimensional spheres, or S^2 x S^2,
S^2 x S^4, S^2 x S^6, and S^6 x S^6, with suitable almost complex
structures. In each case, we describe families of conformal classes of almost
Hermitian metrics relative to them, and some tensorial quantities of relevance
associated such structures. In the latter three cases, we show that with the
metrics we use, these Riemannian manifolds do not carry integrable orthogonal almost complex structures.

9/27: Prof. Zhixu Su and Aleksandar Milivojevic
Title: Smooth or almost complex manifolds with prescribed Betti numbers
Abstract:
Prescribing a sequence of Betti numbers (or more specifically the rational
homotopy type), is there any almost complex manifold realizing the algebraic
data? We will discuss the most basic nontrivial case where the sum of Betti
numbers is three. Rational surgery reduces the problem to finding
characteristic numbers satisfying certain integrality conditions. We will
firstly discuss the smooth case, and then prove the nonexistence of any
almost complex structure on such a manifold if the dimension is greater than
4. We will also provide a general realization theorem for the almost complex case.

10/4: Prof. Mehdi Lejmi (BCC CUNY)
TBA
Abstract:

10/11: Xujia Chen
Title: TBA
Abstract:

10/18: Qian Chen
Title: TBA
Abstract:

10/25: Prof. Fei Ye (Queensborough)
Title: TBA
Abstract:

11/8: Prof. Michael Albanese
Title: TBA
Abstract:

11/15: Prof. Yury Ustinovskiy (NYU)
Title: TBA
Abstract:
Spring 2019
Fall 2018
Spring 2018
Fall 2017
