METU Mathematics Seminars
Spring 2016


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


March 3
Özcan Yazıcı
Texas A&M University at Qatar
Extension of plurisubharmonic functions with logarithmic growth

March 10
Middle East Technical University
Dynamical systems and chaos
We will discuss why the 21st century may be considered by mathematicians as an age of biology, in particular, investigation of brain activity; why dynamical systems theory can be divided into the prechaotic era and the chaotic era of development; what the next focus of applications of nonlinear dynamics is; why chaos is important in this new era of biology and brain activity; why chaos was not needed in the 20th century so much; how chaos is related to information processing and consequently for robotics, brain activity and chaotic computations; and what the role of self-organization for brain activity is. We will provide information about our own research regarding the above problems.

March 17
Texas A&M University
Condition Number for Random Polynomial Systems
The condition number of a polynomial system measures the sensitivity of its roots to perturbations in the coefficients. We study the condition number of random polynomial systems for a broad family of distributions. Our work is motivated by Smale's 17th problem on the complexity of polynomial system solving. We present a brief overview of current state in Smale's 17th problem then proceed with our recent results on average conditioning. This is joint work with J.Maurice Rojas and Grigoris Paouris.

March 24
Middle East Technical University
Bivariate polynomial mappings associated with simple complex Lie algebras
The Chebyshev polynomials, which have remarkable dynamical properties, can be associated with the rank-1 simple complex Lie algebra A1. There are three families of bivariate polynomial mappings associated with the rank-2 simple complex Lie algebras A2, B2 and G2. In this talk, we will focus on the fixed points of these maps and give an application in the theory of finite fields.

March 31
Hacettepe University
Codes on toric varieties and Hilbert function
After we introduce basics of linear codes, we talk about evaluation codes defined on toric varieties. We show how multigraded Hilbert functions can be used to compute dimensions of these codes and finish by giving formulas for the dimensions of some particular codes.

April 7
Middle East Technical University
Unpredictable motions and functions
As we predicted in our previous papers and talks, the row of motions: equilibrium, periodic, quasi-periodic, almost periodic, recurrent and Poisson stable motions can be prolonged by a new type of dynamical behaviour. Recently, together with Dr. Mehmet Onur Fen, we have completed the chain of motions by an unpredictable motion. It is based on the concept of Poisson stability (introduced by Poincare) and uti- lizes a new property, which we call sensitivity. This is a new definition, since the former concerns a family of functions, but we say about sensi- tivity of a single motion. Moreover, unpredictable functions have been introduced as unpredictable points of the Bebutov dynamics. The new concept opens a door for further developments in the theory of differen- tial equations, theory of functions, topology and functional analysis in a similar way to that they have been stimulated by the previous type of functions in the row.

April 14
Middle East Technical University
Chemistry Department
From Sumerian chemists and schools to universities
Earliest chemists were cave man who tanned leather to cover their bodies. They also produced pigments to paint figures on the walls of caves. The oldest cave paintings found in Nerja Caves (35 miles east of Malaga-Spain) are 42 thousand years old. They were painted by Neanderthals.

Twenty thousand years ago. Stone Age men marked bones or sticks to keep records of the amount of goods exchanged. Ten thousand years ago, clay tokens started to be used for keeping records of trade. These tokens led to the invention of numbers. Later Sumerians invented writing (3100 B.C.) and then Egyptian hieroglyphs were developed. There were not enough people who knew how to read and write. Sumerians opened the first schools in the world to educate the scribes (clerks). Sumerian school system became a model for the rest of the world. The level of knowledge of the ancient civilization was not known after they disappeared until the decipherment of hieroglyphs. Later cuneiform inscriptions (Sumerian) were also deciphered. These discoveries made it possible to see the high levels of chemical technologies, mathematics, astronomy and medicine developed by Sumerians, Babylonians and Egyptians. There were no schools in Greece until 450 B.C. or in Europe until 600 A.D. Abbasid and Umayya Caliphs ruled Middle East, North Africa and Cordoba in South of Spain (Andalus) for centuries. They flourished science and education once more, many centuries after Sumerians. Al-Khwarizmi's book (Al-Kitab al mukhtasar fi hisab al-jabr wa-l-muqabala) was the main source for the development of modern algebra. Jabir Ibn Hayyan was the top chemist during Abbasid era. All his books were translated to Latin and to European languages. They were used in Europe for centuries. Avicenna's book Al-Qanoon fi al-Tibb (Law of Medicine) was used in the Medical Schools of Europe until 1650. Nalanda which was founded in 427 A.D. in India is claimed to be the oldest university. Bologna which was founded in 1088 in Italy is universally accepted to be the oldest university.

Sumerians were the first civilization to establish the basic principles of education and discovering most of the early techniques of chemistry, math and medicine.

April 21
University of Isfahan
Frankl's conjecture holds for subgroup lattices

April 28 (İkeda Research Award) at 15:30

Türker Bıyıkoğlu
 
Süleyman Demirel University
Çizgelerde Castelnuovo-Mumford Regülarite Hesapları

May 5
Akdeniz University
Evaluation of Euler-like sums

May 12
Middle East Technical University
Stable Ulrich bundles on Fano 3-folds with
Picard number 2

May 26
University of Brasilia
About length of a finite group
Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. In recent joint work with E. Khukhro we defined the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. In particular, such bounds played important role in the Hall-Higman reduction theorem for the restricted Burnside problem. In the talk several new results on λ(G) will be discussed.

June 2