**ODTÜ-BİLKENT Algebraic Geometry Seminar
All past talks
ordered according to speaker and
date**

**2010 Spring Talks**

- 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. -
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). -
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. -
Bilkent, 19 March 2010 Friday, 15:40

**Alexander Degtyarev**-**[***Bilkent University***]-**Dihedral covers of trigonal curves**Abstract:**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. -
Bilkent, 26 March 2010 Friday, 15:40

**Bedia Akyar-[***Dokuz Eylul University***]-**Prismatic sets in topology and geometry**Abstract:**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. -
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 S^{1}x S^{1}to S^{2}is homotopically trivial, where S^{k}is the unit sphere in R^{k+1}. -
ODTU, 16 April 2010 Friday, 15:40

**Ali Kemal Uncu**-**[***TOBB ETU***]****-**_{2}(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 SL_{2}(Z). We will work with the Riemann surface related to the congruence subgroup of SL_{2}(Z), define modular symbols and give the relation between modular symbols and Fourier coefficients of modular forms. -
ODTU, 30 April 2010 Friday, 15:40

**Ergün Yalçın**-**[***Bilkent University***]****-**Koszul Resolutions and the Lie Algebra Cohomology**Abstract:**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. -
Bilkent, 7 May 2010 Friday, 15:40

**Özgün Ünlü**-**[***Bilkent University***]****-**Homologically trivial group actions on products of spheres**Abstract:**In this talk, I will discuss some constructions of free group actions on products of spheres with trivial action on homology. -
ODTU, 14 May 2010 Friday, 15:40

**Hamza Yeşilyurt**-**[***Bilkent University***]****-**Rogers-Ramanujan Functions**Abstract:**We present several identities for the Rogers-Ramanujan functions along with their partition theoretic interpretations and conclude with our recent work on such identities. -
Bilkent, 28 May 2010 Friday, 15:40

**Mutsuo Oka**-**[***Tokyo University of Science***]****-**Polar weighted homogeneous polynomials and mixed Brieskorn singularity**Abstract:**

**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 A-building at
Bilkent.**

2000-2001 Talks (1-28), 2001 Fall Talks (29-42), 2002 Spring Talks (43-54), 2002 Fall Talks (55-66)

2003 Spring Talks (67-79), 2003 Fall Talks (80-90), 2004 Spring Talks (91-99), 2004 Fall Talks (100-111)

2005 Spring Talks (112-121), 2005 Fall Talks (122-133), 2006 Spring Talks (134-145), 2006 Fall Talks (146-157)

2007 Spring Talks (158-168), 2007 Fall Talks (169-178), 2008 Spring Talks (179-189), 2008 Fall Talks (190-204)

2009 Spring Talks (205-217), 2009 Fall Talks (218-226), Seminar Homepage