ODTÜBİLKENT Algebraic Geometry Seminar
(See all past talks
ordered according to speaker and
date)
2010 Fall Talks
Abstract: The Alexander module of an algebraic curve is a certain purely algebraic invariant of the fundamental group of (the complement of) the curve. Introduced by Zariski and developed by Libgober, it is still a subject of intensive research. We will describe the Alexander modules and Alexander polynomials (both over Q and over finite fields F_{p }) of a special class of curves, the so called generalized trigonal curves. The rational case is closed completely; in the case of characteristic p>0, a few points remain open. (Conjecturally, all polynomials that can appear are indeed listed.) Unlike most known divisibility theorems, which rely upon the degree and the types of the singularities of the curve, our bounds are universal: essentially, the Alexander module of a trigonal curve can take but a finitely many values. 
Abstract: The curious history of Fermat's Last Theorem starts with Fermat's famous marginal commentary. The quest for the solution of this problem has created theories which affect all of mathematics. In this seminar, we will talk about Ribet's theorem which states that modularity theorem (previously known as TaniyamaShimura conjecture) implies Fermat's Last Theorem. A central role in Ribet's proof is played by elliptic curves introduced by Frey. 

On 1315 October, we are having an Algebra and Number Theory Symposium
in
honor of Prof Mehpare Bilhan's retirement.
There will be no Algebraic Geometry talk this week.

Bilkent, 22 October 2010 Friday, 15:40
Christophe Eyral[Aarhus University] 
A short introduction to Lefschetz theory
on the topology of algebraic varieties
Abstract: 

29 October is Republic Day, a national day for Turkey. No talks!

Bilkent, 5 November 2010 Friday, 16:00
Muhammed Uludağ[Galatasaray University]  The Groupoid of
Orientation Twists
Abstract: This is an essay to define a higher modular groupoid. The usual modular groupoid of triangulation flips admits ideal triangulations of surfaces of fixed genus and punctures as objects and flips as morphisms. The higher groupoid of orientation twists admits usual modular groupoids as its objects. 
ODTU, 12 November 2010 Friday, 15:40
İnan Utku Türkmen[Bilkent University]  An
Indecomposable Cycle on Self Product of Sufficiently General
Product of Two Elliptic Curves
Abstract: The group of indecomposables is too complicated to compute in general and the results in literature are cenrered around proving that this group is nontrivial or in certain cases finitely generated. In this talk I will focus on the group of indeconposables of self product of sufficiently general product of two elliptic curves, namely; CH^{3}_{ind}(E_{1}x E_{2} x E_{1} x E_{2}). I will review the results in literature related with this group and sketch an alternative proof for nontriviality of this group using a constructive method. 

1619 November is a religious holiday in Turkey. No talks!

ODTU, 26 November 2010 Friday, 15:40
Mehmetcik Pamuk[ODTU]  scobordism classification of
4manifolds
Abstract: In this talk we are going to show how one can use the group of homotopy selfequivalences of a 4manifold together with the modified surgery of Matthias Kreck to give an scobordism classification of topological 4manifolds. We will work with certain fundamental groups and give scobordism classification in terms of standard invariants. 
Bilkent, 3 December 2010 Friday, 15:40
Ergün Yalçın[Bilkent University]  Productive elements
in group cohomology
Abstract: I will give the definition of a productive element in group cohomology and describe a new approach to productive elements using Dold's Postnikov decomposition theory for projective chain complexes. The motivation for studying productive elements comes from multiple complexes which is an important construction for studying varieties of modules in modular representation theory. 
ODTU, 10 December 2010 Friday, 15:40
Mustafa Kalafat[University of Wisconsin at Madison and ODTU]

Hyperkahler manifolds with circle actions and the GibbonsHawking Ansatz
Abstract: We show that a complete simplyconnected hyperkahlerian 4manifold with an isometric triholomorphic circle action is obtained from the GibbonsHawking ansatz with some suitable harmonic function. 
Bilkent, 17 December 2010 Friday, 15:40
Kürşat Aker[Feza Gürsey]  Multiplicative Generators
for the Hecke ring of the Gelfand Pair (S(2n), H(n))
Abstract: For
a given positive integer n, Gelfand pair (S(2n), H(n)) resembles the
symmetric group S(n) in numerous ways. Here, H(n) is a hyperoctahedral
subgroup of the symmetric group S(2n). In this talk, we will exhibit a new
similarity between the Hecke ring of the pair (S(2n), H(n)) and the center
of the integral group ring of S(n). 
ODTU, 24 December 2010 Friday, 15:40
Ali Sinan Sertöz[Bilkent]  Counting the number of
lines on algebraic surfaces
Abstract: This is mostly an expository talk on the problem of counting the number of lines on an algebraic surface. The problem is to respect the rigidity of the line as opposed to accepting all rational curves as lines. Surprisingly some of the work done by Segre has not yet been matched by contemporary techniques. We will summarize what is known and speculate about what can be known! 

31 December afternoon is no time to hold seminars on this planet! No
talks!

ODTÜ talks are either at Hüseyin
Demir
Seminar room or at Gündüz İkeda seminar room at the Mathematics building of ODTÜ.
Bilkent talks are at room 141 of Faculty of Science Abuilding at
Bilkent.
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