Seminar on Geometry 

Spring 2016, ODTÜ, Ankara

Time / Location: Fridays 2:15 / M-215

Schedule of talks

 

TIME              SPEAKER                  TITLE
Feb 6-7
Sat-Sun, 9:00

Mobbing Temel Analiz Uzmanlık Eğitimi Konferansı
Feb 9
Tue, 2:00

Spektral Diziler A
Feb 11
Wed, 1:00
Aleksandra Borówka
C-map construction
Feb 12
Fri, 3:00
Pawel Borówka
Non-simple principally polarised abelian varieties
Talk at Hacettepe University
Feb 19
Fri, 2:15
Conformal Structures on Tori (Review)
Feb 26
Fri, 2:15
Spectral Sequences 11

3:30
Conformal Structures on Tori (Review)
March 4
Fri, 1:20
İlker Savaş Yüce Jorgensen's Inequality and purely loxodromic 2-generator free Kelinian groups
(Bu konuşma Çankaya Üniversitesinde olacaktır)
March 10
Fri, 2:40
İlhan İkeda
(Yeditepe)
Axiomatic Topological Quantum Field Theory after Atiyah and Segal
In Physics Department, Cavid Erginsoy Seminar Room, 3rd floor
March 11
Fri, 2:15
Özgür Kelekçi CP_2 as a gravitational instanton
Mar 19-20
2:15
AMS Meeting at Stony Brook , NY
April 1
Fri, 2:15
Characteristic Classes on Grassmannians 1
April 8
Fri, 2:30
Spectral sequences 12
Apr 15
Fri, 2:15
İptal Einstein-Maxwell Equations 7

3:30
İptal Spectral sequences 13
Apr 22
Fri, 2:30
Lie Algebras and Root Systems 1

4:00
Spectral sequences 14
April 23-24
Sat-Sun, 9:00
Mobbing Temel Analiz Uzmanlık Eğitimi Konferansı
Yer: Ankara Sanayi Odası: Atatürk Bulvarı no:193 Kavaklıdere
Apr 25
Mon, 1:40
Lie Algebras and Root Systems 2

3:40
Hatice Çoban The four-manifold RP^4#RP^4 does not admit any real projective structure
Apr 26
Tue, 1:40
Lie Algebras and Root Systems 3
Apr 29
Fri, 2:30
No Seminar
May 4
Wed, 1:40
Lie Algebras and Root Systems 4
May 6
Fri, 2:30
Lie Algebras and Root Systems 5
May 13
Fri, 2:15
Workshop on Lie groups, algebras, and their and representations
at IMBM, Boğaziçi University
May 18
Wed, 2:00
Lie Algebras and Root Systems 6
May 20
Fri, 2:15
Workshop on Lie groups, algebras, and their and representations
at IMBM, Boğaziçi University
May 25
Wed, 2:00
Lie Algebras and Root Systems 6
May 27
Fri, 2:15
Workshop on Lie groups, algebras, and their and representations
at IMBM, Boğaziçi University
May 30
Jun 9
23rd Gökova Geometry-Topology Conference

Abstracts/Notlar



Lectures on Lie Algebras

In this lecture series we will give elementary talks on Lie Algebras, Root systems, Representations of Lie Algebras, Cartan subalgebra etc. These are intended as a preparation for the "Workshop on Lie groups, algebras, and their and representations" by Mahir B. Can and Selman Akbulut in IMBM. For details and registration to the workshop: http://www.imbm.org.tr/LIE16/LIE16en.html

We will be following the Reference:

R.W.Carter - Lie Algebras and Root Systems.
In Carter, Roger; Segal, Graeme; Macdonald, Ian - Lectures on Lie groups and Lie algebras.
London Mathematical Society Student Texts, 32. Cambridge University Press, Cambridge, 1995.


Bryant, Robert L. Some remarks on G2-structures.
Proceedings of Gökova Geometry-Topology Conference 2005, 75–109, Gökova Geometry/Topology Conference (GGT), Gökova, 2006.


Other useful references are:

Hall, Brian Lie groups, Lie algebras, and representations. An elementary introduction. Second edition.
Graduate Texts in Mathematics, 222. Springer, 2015. xiv+449 pp.

Lie Algebras 1: Lie Algebras. Basic concepts.

Lie Algebras 2: Representations of Lie Algebras. Nilpotent and Soluble Lie Algebras. Example: sl(2,C).

Lie Algebras 3: Cartan subalgebra.

Lie Algebras 4: Cartan decomposition.

Lie Algebras 5: Killing Form. Weyl Group. Dynkin diagrams.




Lectures on Conformal Structures on Riemann Surfaces


In this seminar series we will give elementary talks on moduli space of conformal classes on elliptic curves. Reference:


J.Jost - Compact Riemann Surfaces. Springer-Verlag.

Tori 1: Teichmüller space and Moduli space of conformal structures. Meromorphic functions.

Tori 2-3: Weierstrass p-function. Embedding into CP_2. Elliptic integrals.




Lectures on Spectral Sequences


In this seminar series we will give elementary talks on Serre spectral sequence. Reference:


Hajime Sato - Algebraic Topology: An Intuitive Approach.
S. Akbulut, M. Kalafat - Algebraic topology of G2 manifolds. Expo. Math. 34 (2016), no. 1, 106–129.

SS 1: The Grassmannian G_3 R^6.


Aleksandra2 : I will present some basics about the c-map construcion. I will also discuss some new results.

Pawel : We will start by introducing basic definition and properties of complex abelian varieties. In particular we recall Poincare Reducibility Theorems for abelian varieties that state that an abelian variety is simple or isogenous to a product of abelian varieties of smaller dimensions. Then, we will improve the statement in the following way. Let Is^g_D be the locus in the moduli space of principally polarised abelian varieties of dimension g that contain an abelian subvariety of at most half dimension and restricted polarisation of type D. Then Is^g_D is an irreducible subvariety in the moduli space and the locus of non-simple abelian varieties is the countable union of all Is^g_D. Moreover, in the similar way to Humbert, we will produce equations for Is^g_D in the Siegel upper half-space.

İkeda : We shall briefly review axiomatic TQFT following Atiyah and Segal, and then discuss its possible applications to number theory, in particular to the Langlands Program.

Özgür : We compare some of the properties of CP2 with those of the SU(2) Yang-Mills Instanton and conclude that CP2 may be regarded as a gravitational pseudoparticle surrounded by an event horizon.

H. Çoban : First, we'll talk about extending some geometries to projective geometry. Then we'll remind the developing map and holonomy to show the manifold RP^4#RP^4 admits no real projective structure. Finally, we'll discuss generalizations not admitting a real projective structure with some given restrictions on manifolds.



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