Seminar on Geometry
Spring/Fall 2020, Boğaziçi, İstanbul
Time / Location: Fridays 3:00 / TB130,240 
Schedule of talks
TIME 
SPEAKER 
TITLE 
Jan 611


The 3rd GTWS GeometryTopology Winter School
Week 1 
Jan 1318


Winter School
Week 2 
Jan 2025


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


Winter School
Week 2 
Mar 2 Mon, 3:40 
Talk at İkeda Seminar Room 
Algebra of G_2 Manifolds
ODTÜ GeometryTopology Seminar 
Jul 611


The 5th GTSS GeometryTopology Summer School
Week 1 
Jul 1318

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 TB130.
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 TB240 
On special submanifolds of the Page space
ODTÜBilkent Algebraic Geometry AG Seminar. 
Dec 4 Fri, 3:00 

Locally Conformally Kähler Manifolds 12
A 4dimensional Solvmanifold 
Dec 11 Fri, 3:00 

Locally Conformally Kähler Manifolds 13
SU(2)xS^1 and noncompact 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 1form.
LCK 2: Weyl connection.
LCK 3: Relation with conformal structures:
HermiteWeyl 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 4dimensional Solvmanifold.
LCK 13: SU(2)xS^1, noncompact examples.
LCK 14: Brieskorn & Van de Ven's manifolds.
LCK 15: Generalized Hopf Manifolds.
We will be using the following resources.
References:
 S. Dragomir, L. Ornea 
Locally conformal Kähler geometry.
Progress in Mathematics, 155. Birkhäuser Boston, Inc., Boston, MA, 1998.
 Vaisman, Izu. Some curvature properties of complex surfaces.
Ann. Mat. Pura Appl. (4) 132 (1982), 1–18 (1983).
 Vaisman, Izu. On locally and globally conformal Kähler manifolds.
Trans. Amer. Math. Soc. 262 (1980), no. 2, 533–542.
 Gauduchon, Paul. La 1forme de torsion d'une variété hermitienne compacte.
[Torsion 1forms 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 mutuallyindependent
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, nboyutlu 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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