Seminar on Geometry 

Spring/Fall 2020, Boğaziçi, İstanbul

Time / Location: Fridays 3:00 / TB-130,240

Schedule of talks

 

TIME              SPEAKER                  TITLE
Jan 6-11

The 3rd GTWS Geometry-Topology Winter School
Week 1
Jan 13-18

Winter School
Week 2
Jan 20-25

The 4th CAGWS Complex Geometry Winter School
Week 1
Jan 27-Feb 2

Winter School
Week 2
Mar 2
Mon, 3:40

Talk at İkeda Seminar Room
Algebra of G_2 Manifolds
ODTÜ Geometry-Topology Seminar
Jul 6-11

The 5th GTSS Geometry-Topology Summer School
Week 1
Jul 13-18
Youtube Videos
Summer School
Week 2
Aug 19
Wed, 3:00
Mustafa Kalafat
Algebra of G_2 Manifolds
Talk at IMBM
Sep 11
Fri, 3:00

Locally Conformally Kähler Manifolds 1
Talk at TB-130. Zoom link. Pass: geometry in Turkish
Sep 18
Fri, 3:00
Locally Conformally Kähler Manifolds 2
Sep 25
Fri, 3:00

Locally Conformally Kähler Manifolds 3
New Zoom link with better internet connection. Pass: geometry in Turkish.
Oct 2
Fri, 3:00
Locally Conformally Kähler Manifolds 4
Newer Zoom link. Pass: geometry in Turkish.
Oct 9
Fri, 3:00
Locally Conformally Kähler Manifolds 5
Newest Zoom link. Pass: geometry in Turkish. Meeting ID: 991 1027 7750
Oct 16
Fri, 3:00
Locally Conformally Kähler Manifolds 6
Oct 23
Fri, 3:00
Locally Conformally Kähler Manifolds 7
Oct 30
Fri, 3:00
Locally Conformally Kähler Manifolds 8
Nov 6
Fri, 3:00
Locally Conformally Kähler Manifolds 9
Hopf Manifolds
Nov 13
Fri, 3:00
Locally Conformally Kähler Manifolds 10
Inoue Surfaces
Nov 20
Fri, 3:00
Locally Conformally Kähler Manifolds 11
A Nilmanifold: Generalized Thurston's manifold
Nov 27
Fri, 3:40
Zoom link TBA, Youtube Video
Talk at TB-240
On special submanifolds of the Page space
ODTÜ-Bilkent Algebraic Geometry AG Seminar.
Dec 4
Fri, 3:00
Locally Conformally Kähler Manifolds 12
A 4-dimensional Solvmanifold
Dec 11
Fri, 3:00
Locally Conformally Kähler Manifolds 13
SU(2)xS^1 and non-compact examples
Dec 18
Fri, 3:00
Locally Conformally Kähler Manifolds 14
Brieskorn & Van de Ven's manifolds
Dec 25
Fri, 3:00
Locally Conformally Kähler Manifolds 15
Generalized Hopf Manifolds
Jan 1
Fri, 3:00
No Seminar
Jan 3
Sun, 3:20
Zoom bağlantısından yayın yapılacaktır.
ID: 842 5215 9903 Şifre: Geometri
4 ve yukarısı yüksek boyutlarda Geometri ve Topoloji
Türkiye Matematik Kulübü (TMK). Konuşmanın Videosu

Abstracts/Notlar


Lectures on Locally Conformally Kähler Manifolds

In this learning seminar series we will make an introduction to the locally conformally Kähler (LCK) geometry. A LCK metric is a structure on a complex manifold which falls somewhere between a Hermitian metric and a Kähler metric.

Ingredients of the individual seminars are as follows:

LCK 1: Introduction. Lee form. Torsion 1-form.

LCK 2: Weyl connection.

LCK 3: Relation with conformal structures: Hermite-Weyl structures with vanishing distance curvature. (Complex dimension ≥ 3)

LCK 4: Globally conformally Kähler (GCK) manifolds.

LCK 5: Vaisman's conjectures.

LCK 6: Curvature properties.

LCK 7: Blow up.

LCK 8: Adapted cohomology.

LCK 9: Examples. Hopf manifolds.

LCK 10: Inoue surfaces.

LCK 11: A Nilmanifold: Generalized Thurston's manifold.

LCK 12: A 4-dimensional Solvmanifold.

LCK 13: SU(2)xS^1, non-compact examples.

LCK 14: Brieskorn & Van de Ven's manifolds.

LCK 15: Generalized Hopf Manifolds.

We will be using the following resources.

References:
  1. S. Dragomir, L. Ornea - Locally conformal Kähler geometry.
    Progress in Mathematics, 155. Birkhäuser Boston, Inc., Boston, MA, 1998.

  2. Vaisman, Izu. Some curvature properties of complex surfaces.
    Ann. Mat. Pura Appl. (4) 132 (1982), 1–18 (1983).

  3. Vaisman, Izu. On locally and globally conformal Kähler manifolds.
    Trans. Amer. Math. Soc. 262 (1980), no. 2, 533–542.

  4. Gauduchon, Paul. La 1-forme de torsion d'une variété hermitienne compacte.
    [Torsion 1-forms of compact Hermitian manifolds] Math. Ann. 267 (1984), no. 4, 495–518.

Kalafat : In this talk we will give a discussion on a program which aims to present a combinatorial approach to the exceptional Lie group G2 and its Lie algebra. We give various results about the algebraic structure. We also prove some of the old results in terms of our approach.

Kalafat : Page manifold is the underlying differentiable manifold of the complex surface, obta- ined out of the process of blowing up the complex projective plane, only once. This space is decorated with a natural Einstein metric, first studied by D.Page in 1978.
In this talk, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the same underlying smooth manifold. This talk is based on a joint work with R.Sarı. Related paper may be accessed from https://arxiv.org/abs/1608.03252 .
Despite working on basic submanifolds, we introduce a variety of mutually-independent techniques, like graphic illustrations, physicist computations, teichmüller space, 3- manifold topology, ODEsystems etc. So that should not be confused with dry, computational diff.geo. involving only symbolic manipulations, meaningless mess of equalities followed by equalities. We always consider the global topology of the submanifold for example, and deal primarily with compact examples.

Kalafat : Yüksek boyutlarda geometri konularıyla ilgili bir tanıtım konuşmasıdır. Öncelikle, n-boyutlu kürenin yüzey alanı ve iç hacminin nasıl hesaplanıldığından bahsedeceğiz. İkinci olarak düğümler teorisi ve geometriyle ilgisinden bahsedilecektir. Örneğin Milnor'un teoremine göre, total eğriliği 4pi den büyük olan sicimlerin düğümlü olması gerektiğinden bahsedeceğiz. Hiperbolik düğüm nasıl olur onu anlatacağız. Son olarak, koni kesitlerinin reel projektif uzayda nasıl doğal olarak yattığından, projektif uzay ve Klein şişesinin yatması için niye üst boyutlara ihtiyaç olduğundan bahsedeceğiz. Ayrıca kompleks projektif uzay ve bazı Lie grupların hacminin, üzerine metrik konarak hesaplanabileceğine değineceğiz. Konuşma Türkçe olup, lisans ve üstü öğrencilerine yöneliktir. Konuya uzak olan, ilgilenen öğretim üyeleri de davetlidir.



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