- Bilkent, 19 February 2010, Friday, 15:40
Ali Sinan Sertöz-[Bilkent University]-Grothendieck-Riemann-Roch Theorem
Abstract: We will conclude last term's seminar on K-theory with an application to algebraic geometry by developing Grothendieck's Riemann-Roch theorem. The talk will be expository and will be accessible even to those who do not remember much of last semester's talks!
- ODTU, 26 February 2010 Friday, 15:40
Deniz Kutluay-[Bilkent University]-Jones Polynomial
Abstract: In 1984, V. Jones introduced a new (polynomial) knot invariant by using an operator algebra. Later, it became clear that this polynomial can be obtained by several different methods. We will pick a simple approach, namely defining it by means of the slightly different Kauffman bracket polynomial. We will then consider Jones polynomials of alternating links. In the remaining time, we will finish with the proofs of Tait's conjectures (due to K. Murasugi) by using Jones Polynomial.
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Bilkent, 5 March 2010 Friday, 15:40
Deniz Kutluay-[Bilkent University]-Tait's Conjectures
Abstract: P.G. Tait conjectured, in 1898, that a reduced alternating diagram of a knot achieves the minimum possible number of crossings for that knot (1), and writhe of such diagrams of the same knot is the same (2). We will first give K. Murasugi's proof to (1) which involves usage of Jones polynomial. We will then use the idea of taking parallels of diagrams (due to R.A. Stong) to prove (2).
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ODTU, 12 March 2010 Friday, 15:40
İnan Türkmen-[Bilkent University]- Detecting Indecomposable Higher Chow Cycles
Abstract: Spencer Bloch defined the higher Chow in mid 80's as a "natural" extension of classical Chow groups and analysed basic properties of these groups in terms of maps to Deligne Cohomology, named regulators. There is a subgroup of higher Chow groups, group of indecomposables, of special interest. In this talk I will introduce two different methods to detect indecomposables; regulator indecomposability and filtrations on arithmetic Hodge structures.
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Bilkent, 19 March 2010 Friday, 15:40
Alexander Degtyarev-[Bilkent University]- Dihedral covers of trigonal curvesAbstract: We classify irreducible trigonal curves in Hirzebruch surfaces that admit a dihedral cover and study geometric properties of such curves. In particular, we prove an analog of Oka's conjecture stating that an irreducible trigonal curve admits an S_3 cover if and only if it is of torus type.
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Bilkent, 26 March 2010 Friday, 15:40
Bedia Akyar-[Dokuz Eylul University]- Prismatic sets in topology and geometryAbstract: We study prismatic sets analogously to simplicial sets except that realization involves prisms. In particular, I will mention the examples; the prismatic subdivision of a simplicial set S and the prismatic star of S. Both have the same homotopy type as S. Moreover, I will give the role of prismatic sets in lattice gauge theory, that is, for a Lie group G and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of G. In turn this defines a G-bundle over the prismatic star. This is a joint work with Johan L. Dupont.
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ODTU, 9 April 2010 Friday, 15:40
Yıldıray Ozan-[ODTU]- Algebraic K-theory in the study of regular maps in real algebraic geometry
Abstract: After introducing some preliminary material about real algebraic varieties I will try to summarize how algebraic K-theory is used to study regular maps between real algebraic varieties. Namely, I will talk about the results of Loday and Bochnak-Kucharz which mainly show that regular maps between certain products of spherees are all null-homotopic. For example, Loday showed that any regular map from S1 x S1 to S2 is homotopically trivial, where Sk is the unit sphere in Rk+1.
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ODTU, 16 April 2010 Friday, 15:40
Ali Kemal Uncu-[TOBB ETU]- Modular symbols on congruence subgroups of SL2(Z)Abstract: The talk will be about finding the Fourier coefficients of a modular form of the given even weight on a congruence subgroup of SL2(Z). We will work with the Riemann surface related to the congruence subgroup of SL2(Z), define modular symbols and give the relation between modular symbols and Fourier coefficients of modular forms.
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ODTU, 30 April 2010 Friday, 15:40
Ergün Yalçın-[Bilkent University]-Koszul Resolutions and the Lie Algebra CohomologyAbstract: Cohomology of a Lie algebra is defined both as the cohomology of its universal algebra and via a Koszul resolution. I will introduce both of the definitions and discuss their equivalence. Then, I will show how the Lie algebra cohomology appears in the integral cohomology calculation of a group extension.
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Bilkent, 7 May 2010 Friday, 15:40
Özgün Ünlü-[Bilkent University]- Homologically trivial group actions on products of spheresAbstract: In this talk, I will discuss some constructions of free group actions on products of spheres with trivial action on homology.
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ODTU, 14 May 2010 Friday, 15:40
Hamza Yeşilyurt-[Bilkent University]-Rogers-Ramanujan FunctionsAbstract: We present several identities for the Rogers-Ramanujan functions along with their partition theoretic interpretations and conclude with our recent work on such identities.
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Bilkent, 28 May 2010 Friday, 15:40
Mutsuo Oka-[Tokyo University of Science]-Polar weighted homogeneous polynomials and mixed Brieskorn singularityAbstract:
2010 Fall Talks
- Bilkent, 1 October 2010, Friday, 15:40
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.
- ODTU, 8 October 2010 Friday, 15:40
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 TwistsAbstract: 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.
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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-manifoldsAbstract: 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.
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Bilkent, 3 December 2010 Friday, 15:40
Ergün Yalçın-[Bilkent University] - Productive elements in group cohomologyAbstract: 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.
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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.
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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).
Multiplicative generators for centers of integral symmetric groups were first identified by Farahat and Higman, which were later shown to be elementary symmetric polynomials in the celebrated Young-Jucys-Murphy elements by Jucys.
In this talk, we will present a set of multiplicative generators for the Hecke ring of (S(2n), H(n)), affirming a conjecture of Matsumoto, who showed these elements are elementary symmetric polynomials evaluated at odd Young-Jucys-Murphy elements after projecting from the integral group ring of S(2n) to the Hecke ring of (S(2n),H(n)).
This is a joint work with Mahir Bilen Can, Tulane University.
* Reference: http://front.math.ucdavis.edu/1009.5373
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ODTU, 24 December 2010 Friday, 15:40
Ali Sinan Sertöz-[Bilkent] - Counting the number of lines on algebraic surfacesAbstract: 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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2011 Spring Talks
- Bilkent, 18 February 2011, Friday, 15:40
Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences
Abstract: This term we plan to go over the interesting parts of J. McCleary's book, The User's Guide to Spectral Sequences (2nd Edition, 2001). I will begin with some motivation and basic definitions. This may take a few weeks after which many people promised to talk about the wonderful spectral sequences they have met!
- ODTU, 25 February 2011 Friday, 15:40
Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences II
Abstract: We are continuing with J. McCleary's book, The User's Guide to Spectral Sequences (2nd Edition, 2001). I will repeat the basic definitions and work on some simple examples.
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Bilkent, 4 March 2011 Friday, 15:40
Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences III
Abstract: We are continuing with J. McCleary's book, The User's Guide to Spectral Sequences (2nd Edition, 2001). I will start with the second chapter and describe two situations where spectral sequences arise.
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ODTU, 11 March 2011 Friday, 15:40
Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences IV
Abstract: We are continuing with J. McCleary's book, The User's Guide to Spectral Sequences (2nd Edition, 2001). I will summarize the third chapter and discuss convergence of spectral sequences.
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Bilkent, 18 March 2011 Friday, 15:40
Alexander Degtyarev-[Bilkent University] - Leray-Serre spectral sequence I
Abstract: We start exploring the geometric application of the machinery of spectral sequence. As the simplest examples, we consider the spectral sequence(s) of a filtered topological space (as a straightforward generalization of the exact sequence of a pair) and the Serre spectral sequence of a simple fibration.
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ODTU, 1 April 2011 Friday, 15:40
Alexander Degtyarev-[Bilkent University] - Leray-Serre spectral sequence IIAbstract: We will continue exploring the immediate consequences and applications of the Serre spectral sequence. Then we will switch to the Leray spectral sequence, which will be derived as a special case of one of the hypercohomology spectral sequences; in particular, we will show that the Leray (and hence Serre) spectral sequences are natural and retain the multiplicative structure, facts that are not immediately obvious from Serre's construction via skeletons.
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Bilkent, 8 April 2011 Friday, 15:40
Ergün Yalçın- [Bilkent University] -The Lyndon-Hochschild-Serre spectral sequence
Abstract: Let G be a group and H be a normal subgroup of G. Then there is a spectral sequence, called LHS-spectral sequence, which converges to the cohomology of G and whose E_2 term can be expressed in terms of cohomology of H and G/H. I will show how the HLS-spectral sequence can be constructed as a spectral sequence of a double complex and then I will illustrate its usage by doing some group cohomology calculations using it.
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ODTU, 15 April 2011 Friday, 15:40
Ergün Yalçın-[Bilkent University] - Calculating with the LHS-spectral sequence
Abstract: Let G be a group and H be a normal subgroup of G. There is a spectral sequence, called LHS-spectral sequence, which converges to the cohomology of G and whose E_2 term can be expressed in terms of cohomology of H and G/H. In last week's seminar, I showed how the LHS-spectral sequence can be constructed as a spectral sequence of a double complex. This week I will show how this spectral sequence is used to do group cohomology calculations. I plan to bring enough examples to illustrate different situations that one faces while doing calculations with spectral sequences.
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Bilkent, 22 April 2011 Friday, 14:35 (Notice the new time for this talk)
Özgün Ünlü-[Bilkent University] -Atiyah-Hirzebruch spectral sequence
Abstract: Let X be a CW complex and h be a generalized cohomology theory. Atiyah-Hirzebruch spectral sequence relates the generalized cohomology groups h_*(X) with ordinary cohomology groups with coefficients in the generalized cohomology of a point.
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ODTU, 29 April 2011 Friday, 15:40
Yıldıray Ozan-[ODTU] - On Cohomology of the Hamiltonian Gorups
Abstract: Homotopy properties of the group of Hamiltonian diffeomorphisms of symplectic manifolds are far richer than those of the diffeomorphism groups. Abrue, Anjos, Kedra, McDuff ve Reznikov are some of the authors who contributed to the theory. In this talk, I will explain basics of the theory and try to present sample arguments.
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Bilkent, 6 May 2011 Friday, 15:40
Mehmet Akif Erdal-[Bilkent University] - James Spectral Sequence
Abstract: We will construct the James spectral sequence which is a variant of Atiyah-Hirzebruch spectral sequence.
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ODTU, 13 May 2011 Friday, 15:40
Mehmetcik Pamuk-[ODTU] - An Application of Atiyah-Hirzebruch Spectral Sequence
Abstract:
