Seminar on Geometry 

Spring/Fall 2019


Schedule of talks

 

TIME              SPEAKER                  TITLE
Feb 23
Sat, 12:00
Ferit Öztürk
Boğaziçi
Special Linear Group: SL(2,Z)
Talk at METU Arf Auditorium
Feb 25
Mon, 3:40
Mustafa Kalafat
Locally conformally flat metrics on surfaces of general type
Talk at ODTÜ İkeda Room
Feb 26
Tue, 4:00
Özcan Yazıcı
METU
Holomorphic Extension of Mappings between Hypersurfaces
Talk at Bilkent Matematik Bölümü Seminer Odası SA-141
Feb 28
Thu, 3:40
Serge Randriambololona
Bilkent
O-minimality (after van den Dries, Wilkie, ...)
METU General Seminar at İkeda Room
Feb 29
Fri, 3:40
Ali Sinan Sertöz
Bilkent
Arf Rings II
AG Seminar at METU
Mar 4
Mon, 3:40
Elif Medetoğulları
Atılım
On The Torsion Generating Set for Mapping Class Group of Orientable Surfaces
Talk at Bilkent Matematik Bölümü Seminer Odası SA-141
Mar 21
Thu, 3:40
Uğur Gül
Hacettepe
On a tensor product C*-algebra acting on the Hardy space of the bi-disc
with applications to composition operators
General Seminar at METU
Mar 22
Fri, 10:00
Contact Topology Workshop
Hacettepe University, Ankara
Mar 26
Tue, 3:00
Mustafa Kalafat
On special submanifolds of the Page space
Talk at IMBM
Mar 28
Thu, 3:00
Kadriye Nur Sağlam
UC Riverside
Constructions of Lefschetz fibrations using cyclic group actions
Talk at IMBM
May 11 - 12 Frontiers in Several Complex Variables and Functional Analysis
Conference at METU
May 27
Jun 1
26th Gökova Geometry-Topology Conference
Jun 3 - 7 Summer Workshop on 4-manifolds, G2 Manifolds and symplectic manifolds
Workshop at GGTI
Sep 9-15
Mon, 4:00
Lectures on G2 Geometry 1
Sep 16-22
Tue, 4:00
Lectures on G2 Geometry 2

Abstracts



Kalafat : We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold Σg × Σh, the product of two surfaces does not admit any locally conformally flat metric arising from discrete and faithful representations for g ≥ 2 and h ≥ 1. This talk is based on a joint work with Ö.Kelekçi. Related paper may be accessed from arXiv:1810.09020.

Yazıcı : Let M ⊂ CN , M′ ⊂ CN′ be real analytic hypersurfaces and F be a holomorphic mapping on one side of M, continuous M and F(M) ⊂ M′. When N = N′, assuming that M and M′ have some non-degeneracy properties, it is well known that any such mapping F extends holomorphically to the other side of the hyperplane M. When N = N′ = 1, this result is known as Schwarz Reflection Principle. In the case of N′ > N, a very little is known about the holomorphic extension of such mappings. This extension problem is also related to holomorphic extension of meromorphic mappings of hypersurfaces. In this talk, we will review some well known results and mention some recent results about these problems.

Serge : A subset of $\mathbb R^n$ is said to be semi-algebraic if it can be described by a finite system of polynomial equalities and inequalities. The collection of semi-algebraic sets enjoys stability by many natural operations (taking the topological closure, projecting,...) making it a rich tool to use, and at the same time its objects satisfy geometric theorems (stratification in smooth manifolds,...) that allow to keep control on their behaviour. O-minimality is an axiomatic approach which captures many of these features of semi-algebraic geometry. This axiomatic generalization is successful in at least two sense: it preserves most of the nice properties of semi-algebraic geometry, and at the same time it has many natural witnesses that allow to "export" these properties outside of the algebraic world (though proving that these witnesses are indeed witnesses is a very difficult problem in general). I will give an overview of results concerning these two aspects of o-minimality (tame behaviour and natural examples) and if time permits try to explain how o-minimality gives perspectives on some aspects of the theory of ODE and how it also is used to prove some results in number theory.

Sertöz : I will first describe the structure of the local ring of a singular branch and explain how the blow up process affects it. Then I will describe, aprés Arf, how the multiplicity sequence can be recovered, not from this ring but from a slightly larger and nicer ring which is now known as the Arf ring. The process of finding this nicer ring is known as the Arf closure of this ring. Finally I will explain how Arf answered Du Val's question of reading off the multiplicity sequence from the local ring.

Elif : The minimal number of generating set for a mapping class group of an orientable surfaces is known as 2g+1. But the Dehn twists used here have infinite order. The problem of finding the minimum number of torsion elements that generate the mapping class group of an orientable surfaces has still open parts. In this talk, I will review the results about the problem and mention a small upgrade about a torsion generating set for lower genus case.

Gül : In this talk we will be concerned with a tensor product C*-algebra generated by Toeplitz operators with QC(quasi-continuous) symbols and Fourier multipliers acting on the Hardy space of the bi-disc. An exact characteriztion of Fredholmness of certain linear algebraic combination of Toeplitz operators and Fourier multipliers will be given. As an application, an exact characterization of the essential spectrum of a "quasi-parabolic" composition operator acting on the Hardy space of the bi-disc will be given. This is the result of a joint work with B.B. Koca of Istanbul University.

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.

Sağlam : We construct families of Lefschetz fibrations over S 2 using finite order cyclic group actions on the product manifolds Sg x Sg for g>0. We also obtain more families of Lefschetz fibrations by applying rational blow-down operation to these Lefschetz fibrations. This is joint work with Anar Akhmedov.



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