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

**2009 Fall Talks**

- Bilkent, 2 October 2009 Friday 15:40

**Aslı Güçlükan--**Vector Bundles and their classification

**Abstract:**The aim of this talk is to give the necessary background material on vector bundles to introduce the topological K-theory. We also explain the classification theorem for vector bundles. This talk is accessible to graduate students at any level. - Bilkent, 9 October 2009 Friday, 15:40

**Aslı Güçlükan--**Introduction to topological K-theory

**Abstract:**Last week we discussed the basic properties of vector bundles over a compact base space X to introduce the topological K-theory. The set of isomorphism classes of vector bundles on X forms a commutative monoid. The idea of K-theory of X is the completion of this monoid to a ring. In this talk, we will discuss basic concepts in K-theory. - ODTU, 16 October 2009 Friday, 15:40

**Yıldıray Ozan-**On Bott periodicity theorem

**Abstract:**This is going to be an introductory talk to Bott's periodicity theorem. - Bilkent, 23 October 2009 Friday, 15:40

**İnan Utku Türkmen-**Introduction to Algebraic K-Theory

**Abstract:**This is going to be a introductory talk to algebraic K-theory. I will introduce algebraic K-theory and discuss some basic properties of it. I will give the sketch of the proof of Swan'a theorem, which gives us the relation between topological and algebraic K-theories. - ODTU, 6 November 2009 Friday, 15:40

**İnan Utku Türkmen-**Introduction to Algebraic K-Theory II: K_{1}of rings

**Abstract:**In this introductory talk we will define K_{1}of rings and discuss their basic properties. - Bilkent, 13 November 2009 Friday, 15:40

**Ergün Yalçın-**Wall's finiteness obstruction and its generalizations

**Abstract:**As one of the topological applications of algebraic K-theory, I will introduce Wall's finiteness obstruction which is defined as the obstruction for a finitely dominated space to be homotopy equivalent to a finite CW-complex. Then, I will discuss the orbit category version of Wall's finiteness obstruction. - ODTU, 4 December 2009 Friday, 15:40

**Ali Sinan Sertöz-**K_{0 }and_{1 }of categories

**Abstract:**Following Rosenberg, we will describe the K theory of certain categories and talk about conditions under which we can use a more `reasonable' collection of modules instead of projective modules and still get the same K theory. This will eventually be applied to discuss Grothendieck's Riemann-Roch theorem but that may be left to the next talk if time runs up. - Bilkent, 11 December 2009 Friday, 15:40

**Özgün Ünlü-**Spheres which are H-spaces

**Abstract:**We will talk about the proof of the well-known fact that an n-dimensional sphere is an H-space if and only if n=0, 1, 3, or 7. - Bilkent, 18 December 2009 Friday, 15:40

**İzzet Coşkun-**Birational geometry of moduli spaces

**Abstract:**The Kontsevich moduli space of stable maps is the central object in Gromov-Witten theory. In this talk, I will discuss its birational geometry and describe how to run Mori's program on small degree examples. I will focus on a few concrete examples.This is joint work with Dawei Chen and builds on joint work with Joe Harris and Jason Starr.

**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.**