METU Mathematics Seminars
Spring 2013


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


February 21
Seher Tutdere
Institute of Applied Mathematics, METU
On Towers of Function Fields Over Finite Fields

February 28
Koc University
Sinan Unver from the Department of Mathematics at Koc University is rewarded to the Ikeda Research Award 2012. The ceremony will be at 15:30.
Motives and cyclotomic p-adic multi-zeta values
One of Grothendieck's most fundamental ideas in terms of the applications of algebraic geometry to arithmetic is the theory of motives. In the first part of the talk, I will describe the main properties of this category without going into too much technical detail. In the second part of the talk, I will talk about some results on cyclotomic p-adic multi-zeta values, which are p-adic realizations of some mixed Tate motives.

March 14
Middle East Technical University
Rational function analogue of Dickson polynomials
We give an alternative computation of the value set of Dickson polynomials by using a singular elliptic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value set of rational functions related with isogenies of elliptic curves with complex multiplication.

March 21, M203
Middle East Technical University
Tunneling phenomena from radioactivity to the atomic bomb
You never observe a mathematician sitting in his office, playing with his Klein bottle disappear suddenly and instantaneously appear as a physicist in the physics building. Yet, the life and the mere existence of a mathematician depends on such classically forbidden tunnelings at the microscopic level. For example the first step in the energy production mechanism of the sun is the tunneling of a proton near another proton and then turning into a neutron. I will discuss the quantum mechanics of this ubiquitous tunneling process and how it led to the nuclear energy and the atomic, thermonuclear bombs. Listener discretion is advised.

March 28
Hacettepe University
Automorphisms of Some Matrix Rings
We describe the automorphism group of certain radical matrix rings.

April 4 (cancelled)
Middle East Technical University
Restricted Modules and Conjectures for Modules of Constant Jordan Type
Let A be an abelian p-group of exponent at least p^t, and k be an algebraically closed field of characteristic p. We define the class of restricted k[A]-modules and give a method to construct k[A]-modules of constant p^t-Jordan type. Hence, we show that many Jordan types are realizable. For restricted k[A]-modules, we generalize several theorems by Benson, and verify a generalization of conjectures by Suslin and Rickard. We state new conjectures giving constraints on Jordan types.

April 11
Koc University
A central function in analytic number theory: Mobius function
I will discuss the history and motivation for working with the Mobius function. Connections between partial sums of Mobius function and Riemann hypothesis (RH) will be emphasized. Cancellation and asymptotic orthogonality properties will be mentioned. I will also discuss very recent results of Tao and related results of mine as time permits.

April 18
Strasbourg University
Surfaces of degree 4 in the real projective space
A surface of degree 4 in the real projective space of dimension 3 is a homogeneous polynomial of degree 4 in 4 variables, with real coefficients, and considered up to multiplication by a nonzero real number. The set of real points of the surface is the set of zeros of the polynomial in the real projective space. A natural classification of surfaces in the real projective space is the classification up to homeomorphism. A finer classification is the one up to isotopy, i.e., up to homeomorphism of the real projective space. An even finer classification is the one up to rigid isotopy, i.e., up to a path in the space of nonsingular surfaces of degree 4. We will discuss these classifications and how we can obtain this information in the case of nonsingular surfaces of degree 4, and in the case of singular surfaces of degree 4 with a nondegenerate double point (which is the simplest singularity that a surface can have).

April 25
Firat Arikan
Middle East Technical University
Existence of Lefschetz Fibrations on (Wein)Stein Domains
After a brief introduction to the subjects, we will sketch the proof of the fact that (up to diffeomorphism) every (Wein)Stein domain W of dimension 2n+2>4 admits a Lefschetz fibration such that the corresponding boundary open book is compatible with the induced contact structure on the boundary of W. This is a joint work with Selman Akbulut.

May 2
Mehpare Bilhan
Middle East Technical University
Hasse-Arf Theorem
Hasse-Arf Theorem can be summarized as follows: "The breaks in the upper numbering of the ramification groups in abelian extensions of local fields occur at integers.". In the talk, we shall first summarize the main results of local class field theory, the ramification groups, and then state the Hasse-Arf Theorem.

May 9
Galatasaray University
Cark Groupoids and Thompson's Groups
(on-going work with Ayberk Zeytin)
We introduce and study an analogue of Thompson's group T. This group appears as the fundamental group of the so-called cark groupoid, whose objects are certain infinite ribbon graphs called carks. These are graphs can be naturally identified with the set of narrow ideal classes in real quadratic number fields. They are canonically embedded in conformal annuli, with a unique cycle, with several Farey tree components attached to this cycle. Morphisms of the cark groupoid are generated by flips. They can be identified with the set of indefinite binary quadratic forms. Objects of this groupoid can be naturally identified with classes of indefinite binary quadratic forms. We aim to show that the group associated to the cark groupoid is an infinite extension of Thompson's group. Along the way we also study three simpler analogues leading to Thompson's group F and to some finite extensions of T. An open question is: what kind of arithmetic information can one extract out of this group?

May 16
Middle East Technical University
A new relativistic model on curved spacetimes: Relativistic Burgers equations and numerical experiments
We identify a hyperbolic balance law posed on a curved spacetime that shares the same Lorentz invariance property as the one satisfied by the Euler equations of relativistic compressible fluids. This model is unique up to normalization and converges to the standard inviscid Burgers equation in the limit of infinite light speed. We observe that, both the standard inviscid Burgers equation and our relativistic generalizations are derived from the Euler system of relativistic compressible flows on a spacetime. The proposed models are referred to as relativistic Burgers equations on curved spacetimes and provide us with simple models on which numerical methods can be developed and analyzed. We introduce a finite volume scheme for the approximation of discontinuous solutions to these relativistic Burgers equations. Our scheme is formulated geometrically and it preserves static solutions. Numerical experiments are presented which demonstrate the convergence of the proposed finite volume scheme.

May 23
Middle East Technical University
Centralizers of elements in simple locally finite groups
A group G is called a locally finite group if every finitely generated subgroup of G is a finite group. The class of locally finite groups are the natural generalization of finite groups. We will give examples of simple locally finite groups and centralizers of some subgroups in the special cases. The talk will be a general survey of some known results and recent results. Finally we will mention some open questions.