METU Mathematics Seminars
Fall 2011


Previous Seminars: Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011.


October 6
Cem Guneri
Sabanci University
A Family of Maximal Curves
A curve defined over a finite field is called maximal if its number of rational points meets the Hasse-Weil upper bound. The Hermitian curve H is the most important example of a maximal curve since almost all known examples of maximal curves are covered by H. In 2009, Giulietti and Korchmaros constructed the first example of a maximal curve which is not covered by H. In this talk, we will present the Giulietti-Korchmaros (GK) curve and its generalization (by Garcia-Guneri-Stichtenoth). The automorphism group of the generalized GK curve is also determined recently (by Guneri-Ozdemir-Stichtenoth). Depending on time, we may also discuss the automorphism group.

October 13
Gerhard Wilhelm Weber
Institute of Applied Mathematics, Middle East Technical University
How Can We Anticipate Dynamics under Various Time and Uncertainty Assumptions? Motivations and Applications in Finance, Education, Biology, Medicine and Economics Some Recent Contributions Supported by Applied Mathematics
This presentation introduces recent research efforts and results in identifying and predicting time-dependent processes, with various degrees of model discontinuity and uncertainty. This generalization is gradually unfolded, while always motivated by real-world challenges and applications of them. We aim at displaying joy and interest in state-of-the art applied mathematics and to invite to education, research and developing our countries by its help, in our scientific community. In fact, we try to "make appetite" for this!

October 20
Asli Guclukan
Bilkent University
Obstructions for constructing equivariant fibrations
The aim of this talk is to introduce an obstruction theory for constructing G-equivariant fibrations where G is a finite group. Constructing equivariant fibrations is an important step in the construction of free group actions on finite CW-complexes which are homotopy equivalent to a product of spheres. We also discuss some conjectures about finite group actions on products of spheres and on finite complexes homotopy type of a product of spheres.

October 27
Turgay Kaptanoglu
Bilkent University
Operator-Theoretical Considerations on Weighted Symmetric Fock Spaces

November 17
Tolga Karayayla
University of Pennsylvania
Automorphism groups of rational elliptic surfaces with section
In this talk I will describe the structure of the automorphism groups of rational elliptic surfaces with section defined over the field of com- plex numbers.. While generic fiber of the map from the surface to the base curve is a smooth elliptic curve, there are also singular fibers. The configuration of those singular fibers on the elliptic surface gives very important information about the automorphism group. I will explain how the automorphism groups of rational elliptic surfaces are classified with respect to the configurations of singular fibers. Generally, the au- tomorphism group is the semi-direct product of the Mordell-Weil group and the subgroup of automorphisms preserving the zero section of the surface. The Mordell-Weil group which is the group of sections has been classified by Oguiso and Shioda. In the talk I will concentrate on how the latter subgroup is determined.

November 20
Ozgür Sarioglu
Department of Physics, Middle East Technical University
Faster than the speed of light?
 

December 1
Sinem Celik
Hacettepe University
Knots in Contact Structures and Open Book Decompositions
Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will introduce basic definitions and examples of open book decompositions. Further, we will discuss the importance of the open books in manifold theory, in particular in contact geometry. After a brief introduction on contact 3-manifolds, we will focus on a class of knots in contact 3-manifolds called Legendrian knots. We will define a new invariant for Legendrian knots using open book decompositions. This talk aims to reach general audience.

December 8
Turgay Kaptanoglu
Bilkent University
Operator-Theoretical Considerations on Weighted Symmetric Fock Spaces - Part II

December 15
Cem Tezer
Middle East Technical University
Turkey 1933-1952 : A questionable refuge for exile German mathematicians
I will attempt at evaluating the contribution of the exile German mathematicians to the development of Turkish mathematics in the years 1933-1952. Not only does such an inquiry bring up the question of susceptibility of the Turkish mathematical community to the stimulation that the proximity of these mostly relatively well qualified scientists should entail, but also that of the extent to which the exile Germans themselves were able to continue productive research in their new environment.

December 22
Neil Lambert
CERN Theory Division, Geneva
King's College, University of London
Up from String Theory : The mathematics of branes in String and M-Theory
In this talk I will review String Theory and its non-perturbative formulation as M-theory. These are viewed as the most promising approach to a quantum unified theory of Yang-Mills gauge theories and gravity. Branes, that is objects with extended spatial directions, play a key role. The dynamics of branes are controlled by quantum field theories in a variety of dimensions and involve Lie-algebras and generalizations known as 3-algebras. In addition there is speculation that more exotic topics such as non-Abelian Gerbes and 2-groups must play an important role.