METU Mathematics Seminars
Fall 2015

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 15
M. Gökhan Benli
Middle East Technical University
How Groups Grow
The growth function of a finitely generated group measures how fast the balls in its Cayley graphs grow. This asymptotic invariant attracted a lot of attention starting from M. Gromov's celebrated theorem about groups which grow polynomially. This talk will be a survey of history, open problems and recent developments around this notion. The main focus will be on groups whose growth is intermediate between polynomial and exponential constructed by R. Grigorchuk.
October 22 (Math Club Talk in M13)
Sabancı University
Kainatın Matematiksel Tasvirleri:
Diferansiyel Denklemler
November 5
İbrahim Ünal
Middle East Technical University
Calibrated Geometries and φ-free Submanifolds
Calibrated geometries, introduced by Harvey and Lawson in 1982, are the geometries of calibrated submanifolds, a distinguished type of minimal submanifolds determined by a fixed, closed differential form φ called a calibration on a Riemannian manifold M. A Kähler form ω in complex geometry provides the first rich example of a calibration and calibrated geometries can be viewed as the generalization of Kähler manifolds as they have many similar properties. Recently, the introduction of plurisubharmonic functions on calibrated manifolds, which provides us doing analysis on them very similar to the one on complex manifolds, has made another type of submanifolds very important. These submanifolds are called as φ-free and are the generalization of totally real submanifolds of complex manifolds.

In this talk, I will start with an introduction to calibrated manifolds, and give the most well-known examples coming from special holonomy. Then, I will talk about the geometry and topology of φ-free submanifolds.
November 12
Middle East Technical University
Replication of chaos: Theory and Applications
We will introduce our results on mathematical chaos based on input-output analysis. The novelty achieved in the chaos investigation allow us to to discuss fundamental question of chaos theory existence. It will be shown that chaos analysis brings finite dimensional dynamics close to infinite dimensional one. That replication of chaos can be considered relative to Alan Turing morphogenesis concept as well as Il'ya Prigozhin theory of dissipative structures and synergetics of Herman Haken. Moreover, we will say about our results as a contribution to the self-organization theory. As a particular application you will see how a linear Cantor set can be extended in three dimensional space. Why is the weather unpredicability global? Why is an economical crisis unpredictable and global? What is chaos role for brain activity and robotics? We will consider the questions in the framework of our theory. These and many other aspects of dynamical systems as well as mathematics globally are concerned to what we are busy with last ten years. Some of them can be found in our last book:
M. Akhmet & O. Fen, Replication of chaos in neural networks, economics and physics, Springer & HEP, 2015.
November 19
Middle East Technical University
Problem of Time, Godel's Universe and the Quest for Quantum Gravity
Einstein wrote general relativity, the theory of spacetime and gravity, 100 years ago. Its principles are apparently in conflict with the principles of microscopic physics, that is Quantum Mechanics. I hope to present some review of the problems, especially the the problem of time and causality as exemplified in Godel's solution where one can travel to the past. [Imagine a mathematician going back to his/her youth to learn some physics.]
November 27 - Friday at 15:40

Due to a 60th year organization, Mathematics and love in the age of artificial intelligence by Edward Frenkel on Nov 26 at 14:00, our general seminar will take place on an unusual date. This talk will be joint with ODTÜ-Bilkent Algebraic Geometry Seminar
Mimar Sinan Fine Arts University
Primality via Height Bound
Height functions are of fundamental importance in diophantine geometry. In this talk, we obtain height bounds for polynomial ring over the field of algebraic numbers. This enables us to test the primality of an ideal. Our approach is via nonstandard methods, so the mentioned bounds will be ineffective. We also explain the tools from nonstandard analysis.
December 3
TOBB ETÜ and Wayne State University
Conditioning analysis of nonlocal operators in fractional Sobolev spaces
We study the condition number of the stiffness matrix arising from finite element discretizations of nonlocal integral operators with singular and integrable kernels. Such operators are used in nonlocal diffusion, peridynamics formulation of continuum mechanics, image processing, and phase transition. We quantify of the extremal eigenvalues with respect to all underlying parameters; the horizon, the mesh size, and regularity of the fractional Sobolev space. We prove the sharpness of the proposed quantifications and support the sharpness result with numerical experiments.
December 17
Şükran Demiralp
Tourette Sendromu, Son Gelişmeler ve Yaşadıklarımız
Bu konuşmada günümüzdeki tanımıyla nörogelişimsel bozukluklardan olan Tourette sendromu ve nadir durumları tanıtılacak, bu alanda yapılan bilimsel araştırmalar, toplumdaki farkındalığın arttırılması yolundaki faaliyetler konuşmacının bizzat edindiği deneyimlerin ışığında anlatılacaktır.
December 24
Hyunjoo Cho
Hacettepe University
An almost contact structure on G2 manifolds
Recently, many results are known as studying the contact and almost contact manifolds. In this talk, we first review these two structures on odd-dimensional manifolds. Then we explain an almost contact metric structure on G2 manifolds, and show that when this almost contact metric structure is cosymplectic.
January 7
Oğuz Yayla
Hacettepe University
Unsolvability of certain equations over the ring of integers of cyclotomic number fields
In this talk, the unsolvability of certain equations \alpha\overline{\alpha} = \omega over the ring of integers of cyclotomic number fields whose ring of integers is not a principal ideal domain will be presented. The method is a generalization of the idea of Brock. This method is used for the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson-Hadamard (BH) matrices and (near) conference matrices. We show some new non-existence results for near BH matrices and near conference matrices. The previously known methods for deriving non-existence results will also be presented: vanishing sums of roots of unity and self conjugacy. We wil also mention the contribution of Akyildiz-Guloglu-Ikeda in this direction.

This is a joint work with Arne Winterhof and Volker Ziegler.
University of Magdeburg, Germany
We would like to draw your attention to the series of talks that will be given by Prof. Wolfgang Willems, the details of which are given below. Please note that the final seminar in the series will be the Departmental General Seminar and it will be joint with the Institute of Applied Mathematics.
January 12 (Room S209 at 15:40)

The mathematics of random network coding
January 14 (Room S209 at 15:40)

Rank metric codes
January 19 (Room S209 at 15:40)

Self-dual MRD codes
January 20 (Gündüz İkeda Room at 15:40)

Quasi-projective characters in representation theory