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

**2009 Spring Talks**

- Bilkent, 20 February 2009 Friday 15:40

**Ali Sinan Sertöz--**What is wrong with the proof of the Hodge conjecture?

**Abstract:**Last year a 6 page proof of Hodge conjecture was deposited into the arXives. Later a 7 page revision was posted, see arXiv:0808.1402 This paper uses only the material found in chapter 0 of Griffiths and Harris' Principles of Algebraic Geometry. In this talk we will review this introductory material for the graduate students and then present the arguments of the alleged proof and ask the audience to find the error! - ODTÜ, 27 February 2009 Friday 15:40

**Ali Sinan Sertöz--**Hodge conjecture; is it still open?

**Abstract:**Last week we mentioned a subtle gap in the alleged proof of Hodge conjecture in arXiv:0808.1402. This week we will mention an irrecoverable gap in the*proof*and then give an informal survey of what is know in the Hodge conjecture front. - ODTÜ, 6 March 2009 Friday 15:40

**Deniz Kutluay-**Knot groups

**Abstract:**We will give an old constructive method to find the presentation of the knot group which is a knot invariant and we will finish with some illustrations. - Bilkent, 13 March 2009 Friday 15:40

**Deniz Kutluay-**Fox calculus

**Abstract:**There is a method of finding the group presentation of a tame knot. However, it is not an easy task to distinguish groups given their presentations, even in particular examples. Therefore, one needs to find presentation invariants. We shall first consider the Alexander matrix and elementary ideals of a given finite presentation in a general setup then restrict our attention to knot groups and get knot polynomials which happen to be knot invariants of trivial distinguishability. - Bilkent, 20 March2009 Friday 15:40

**Mesut Şahin-**Toric ideals of simple surface singularities

**Abstract:**We will present a class of toric varieties with exceptional properties. These are toric varieties corresponding to rational singularities of DE type. We show that their toric ideals have a minimal generating set which is also a Groebner basis consisting of large number of binomials of degree at most 4. - ODTÜ, 27 March 2009 Friday 15:40

**Münevver Çelik-**Calculating Alexander polynomials

**Abstract:**We will demonstrate different methods of calculating the Alexander polynomial on several examples. - Bilkent, 3 April 2009 Friday 15:40

**Alexander Degtyarev-**Towards the generalized Shapiro and Shapiro conjecture

**Abstract:**We deal with the following generalized version of the Shapiro and Shapiro total reality conjecture: given a real curve**C**of genus*g*and a regular map**C --> P**of degree^{1}*d*whose all critical points are distinct and real (in**C**), the map itself is real up to a Mőbius transformation in the target. The generalization was suggested by B. and M. Shapiro in about 2005, after the original conjecture was proved, and it was shown that the statement does hold for*g>d*/3+O(^{2}*d*). In the talk, we improve the above inequality to*g>d*/4+O(^{2}*d*).

- ODTÜ, 10 April 2009 Friday 15:40

**Yıldıray Ozan-**J-holomorphic curves in the study of symplectomorphism groups of symplectic 4-manifolds

**Abstract:**In this talk, after I describe algebraic automorphisms group of**P**, I will consider the analogous problem in the category of symplectic topology. I will present some results comparing them with the results in the study of volume preserving diffeomorphisms group. In the remaining time, I will talk about the main technique used in the proof, so called the theory of^{1}xP^{1}**J**-holomorphic curves in symplectic topology and how they are employed in this work.

- Bilkent, 17 April 2009 Friday 15:40

**Alexander Degtyarev-**Real elliptic surfaces and real elliptic curves of type I (joint w/I. Itenberg)

**Abstract:**We attempt to study/classify real Jacobian elliptic surfaces of type I or, equivalently, separating real trigonal curves in geometrically ruled surfaces. (On the way, we extend the notions of type I and being separating to make them more suitable for elliptic surfaces.) We reduce the problem to a simple graph theoretical question and, as a result, obtain a characterization and complete classification (quasi-simplicity) in the case of rational base. (The results are partially interlaced with those by V. Zvonilov.) As a by-product, we obtain a criterion for a trigonal curve of type I to be isotopic to a maximally inflected one.

- ODTÜ, 24 April 2009 Friday 15:40

**İnan Utku Türkmen-**A brief introduction to higher Chow groups

**Abstract:**I will talk about the fundemantal concepts in the study of Higher Chow groups, historical background and main research subjects in this field in relation with classical Hodge Theory. I will demonstrate some of these concepts and methods by discussing in a "genaralization" of Hodge conjecture (so called Hodge-D conjecture) for product of two general elliptic curves.

- Bilkent, 4 May 2009 Monday 15:40
**-- Note the unusual date**

**Fatma Altunbulak Aksu-**Varieties of modules and a filtration theorem

**Abstract:**The variety of a finitely generated kG-module is a closed homogeneous subvariety of the maximal ideal spectrum of the cohomology ring of a finite group G with coefficients in an algebraically closed field k of characteristic p>0. I will give some basic definitions and properties of varieties in group cohomology. Then I will present some results on filtration of modules related to varieties. - ODTÜ, 8 May 2009 Friday 15:40

**Ali Sinan Sertöz-**Preliminaries on motifs

**Abstract:**We will outline the construction of pure motifs, concentrating on the Chow-Kunneth decomposition. Time permiting we intend to describe the transcendental part of the motif of a surface. This is an informal introductory talk.

- Bilkent, 15 May 2009 Friday 15:40

**Muhammed Uludağ-**The Universal Arithmetic Curve

**Abstract:**I will discuss the limit space F of the category of coverings C of the "modular interval" as a deformation retract of the universal arithmetic curve, which is by (my) definition nothing but the punctured solenoid S of Penner. The space F has the advantage of being compact, unlike S. A subcategory of C can be interpreted as ribbon graphs, supplied with an extra structure that provides the appropriate morphisms for the category C. After a brief discussion of the mapping class groupoid of F, and the action of the Absolute Galois Group on F, I will turn into a certain "hypergeometric" galois-invariant subsystem (not a subcategory) of genus-0 coverings in C. One may define, albeit via an artificial construction, the "hypergeometric solenoid" as the limit of the natural completion of this subsystem to a subcategory. Each covering in the hypergeometric system corresponds to a non-negatively curved triangulation of a punctured sphere with flat (euclidean) triangles. The hypergeometric system is related to plane crystallography. Along the way, I will also discuss some other natural solenoids, defined as limits of certain galois-invariant genus-0 subcategories of non-galois coverings in C. The talk is intended to be informal, relaxed and audience friendly.

**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)