Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences
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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! |
Ali Sinan Sertöz-[Bilkent University] - Basics of Spectral Sequences II
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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. |
Bilkent, 4 March 2011 Friday, 15:40
Ali Sinan Sertöz-[Bilkent University] - Basics
of Spectral Sequences III
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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
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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. |
Bilkent, 18 March 2011 Friday, 15:40
Alexander Degtyarev-[Bilkent University] - Leray-Serre
spectral sequence I
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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. |
ODTU, 1 April 2011 Friday, 15:40
Alexander Degtyarev-[Bilkent University] - Leray-Serre
spectral sequence II
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Abstract: 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. |
Bilkent, 8 April 2011 Friday, 15:40
Ergün Yalçın- [Bilkent University] -The
Lyndon-Hochschild-Serre spectral sequence
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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. |
ODTU, 15 April 2011 Friday, 15:40
Ergün Yalçın-[Bilkent University] - Calculating with
the LHS-spectral sequence
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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. |
Bilkent, 22 April 2011 Friday, 14:35 (Notice the new time for this talk)
Özgün Ünlü-[Bilkent University] -Atiyah-Hirzebruch spectral sequence
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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. |
ODTU, 29 April 2011 Friday, 15:40
Yıldıray Ozan-[ODTU] - On Cohomology of the Hamiltonian Gorups
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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. |
Bilkent, 6 May 2011 Friday, 15:40
Mehmet Akif Erdal-[Bilkent University] - James Spectral Sequence
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Abstract: We will construct the James spectral sequence which is a variant of Atiyah-Hirzebruch spectral sequence. |
ODTU, 13 May 2011 Friday, 15:40
Mehmetcik Pamuk-[ODTU] - An Application of Atiyah-Hirzebruch
Spectral Sequence
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