Seminar on Geometry

Summer 2016, ODTÜ, Ankara

Time / Location: (Monday), Wednesday and Fridays 3:00 / M-214

Schedule of talks

 

TIME              SPEAKER                  TITLE
Jun 15
Wed, 3:00
Mustafa Kalafat
Lie Algebras and Geometry 1
Jun 17
Fri, 3:30

Lie Algebras and Geometry 2
Jun 22
Wed, 5:00

Lie Algebras and Geometry 3
Jun 24
Fri, 3:00

Lie Algebras and Geometry 4
Jul 1
Fri, 3:00
Lie Algebras and Geometry 5
Jul 5-9 Ramazan Bayramı
(1.gün, 5 Tem. Salı)

LeBrunfest in Montreal, Canada
Jul 15
Fri, 3:00
Lie Algebras and Geometry 6
Jul 18-22

7th European Congress of Mathematics
Berlin
Jul 29
Fri, 11:30
Lie Algebras and Geometry 7

2:00
Lie Algebras and Geometry 8

3:00
Özhan Genç
(ODTÜ)
Stable Ulrich bundles on Fano 3-folds with Picard number 2
Ph.D. Thesis Defence at Ikeda Room

4:00
Spectral sequences 1
Aug 2
Tue, 2:00
Lie Algebras and Geometry 9
Aug 4
Thu, 3:00
Lie Algebras and Geometry 10
Aug 5
Fri, 2:00
Lie Algebras and Geometry 11
Aug 12
Fri, 2:30
Cancelled Lie Algebras and Geometry 12
Aug 15
Mon, 2:00
Lie Algebras and Geometry 13

Abstracts/Notlar



Lie Algebras and Geometry

In this lecture series we will give elementary talks on Lie Algebras, Root systems, Representations of Lie Algebras, Cartan subalgebra etc.

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: Killing Form.

Lie Algebras 2: Weyl Group.

Lie Algebras 3: Dynkin diagrams.

Lie Algebras 4: Verma Modules Fundamental Weights.

Lie Algebras 5: Weyl character formula. Weyl dimension formula. Examples.

Lie Algebras 6: Review.

Lie Algebras 7: Fundamental representations.

Lie Algebras 8: Simple groups of Lie type.

Lie Algebras 11: Real and compact real forms.


Genç: A vector bundle E on a projective variety X in P^n is Ulrich if for some linear projections X in P^n−1 the direct image of E is trivial. It was conjectured that on any variety there exist Ulrich bundles. In this talk, we studied the construction of stable Ulrich bundles of rank 1 and 2 on Fano 3-folds which are blow-up of P^3 along a genus 3, degree 6 curve



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These activities are supported by Tübitak