Alexander Degtyarev-[Bilkent University] - The Alexander module of a trigonal curve
|
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 Fp ) 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. |
Ömer Küçüksakallı-[ODTU] - Frey Curves and Fermat's Last theorem
|
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 Taniyama-Shimura conjecture) implies Fermat's Last Theorem. A central role in Ribet's proof is played by elliptic curves introduced by Frey. |
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On 13-15 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.
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Bilkent, 22 October 2010 Friday, 15:40
Christophe Eyral-[Aarhus University] -
A short introduction to Lefschetz theory
on the topology of algebraic varieties
|
Abstract: |
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29 October is Republic Day, a national day for Turkey. No talks!
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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 non-trivial 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; CH3ind(E1x E2 x E1 x E2). I will review the results in literature related with this group and sketch an alternative proof for non-triviality of this group using a constructive method. |
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16-19 November is a religious holiday in Turkey. No talks!
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ODTU, 26 November 2010 Friday, 15:40
Mehmetcik Pamuk-[ODTU] - s-cobordism classification of
4-manifolds
|
Abstract: In this talk we are going to show how one can use the group of homotopy self-equivalences of a 4-manifold together with the modified surgery of Matthias Kreck to give an s-cobordism classification of topological 4-manifolds. We will work with certain fundamental groups and give s-cobordism 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 Gibbons-Hawking Ansatz
|
Abstract: We show that a complete simply-connected hyperkahlerian 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking 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! |
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31 December afternoon is no time to hold seminars on this planet! No
talks!
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