Ay: Mart 2019

Hikmet Burak Özcan (DEU)

Tarih ve Zaman: 29/03/2019, Saat:10:00

Yer: B256

Bu konuşmada, ilk olarak bir eğri üzerindeki rasyonel nokta tanımını vererek başlayacağız. Ardından eğriler üzerindeki rasyonel noktaları bulma problemini ele alacağız. Bilinen bir rasyonel noktadan nasıl yeni bir rasyonel nokta bulabileceğimizin tarifini vereceğiz. Daha sonra eliptik eğrilere kısa bir başlangıç yapacağız ve eliptik eğriler üzerindeki rasyonel noktalara değineceğiz. Son olarak da önemli sonuçlardan olan Mordell ve Siegel Teoremlerini konuşacağız. 

Doga Can Sertbaş, Cumhuriyet University

Tarih ve Saat: 22/03/2019, Saat: 10:00

Yer: B256, DEU Matematik Bölümü

In 1947, Erdos gave a lower bound for the diagonal Ramsey numbers R(k,k). His proof contains purely probabilistic arguments where the original problem is not related to the probability theory. This pioneering work of Erdos gave rise to a new proof technique which is so called the probabilistic method. According to this method, one just obtains the existence of a particular mathematical object in a non-constructive way. In this talk, we first introduce the Ramsey numbers and then explain the basics of the probability theory. After mentioning the fundamentals of the probabilistic method, we give several examples from the number theory. In particular using probabilistic inequalities, we show how one can prove some number theoretic results which seem completely unrelated to the probability theory.

Neslihan Güğümcü, Atina Teknik Üniversitesi

Tarih: 15/03/2019, Saat:10:00

Yer: B256, DEU Matematik Bölümü

Özet: Planar curves have been studied since the time of Gauss. Gauss was one of the first to notice that they can be handled combinatorially by codes (named as Guass codes) that are strings of labels encoding self-intersections. Whitney classified all immersed curves up to a topological relation called regular homotopy by using the winding number of immersion maps. In the first half of the 20^th century Reidemeister showed that classical knot theory is equivalent to the study of immersed curves in the plane, whose self-intersections are endowed with a combinatorial structure, with an under/over-data. With this extra structure, regular homotopy needs to transforms into a richer equivalence relation generated by Reidemeister moves. Since then knot theory is a classical subject of topology, bringing us many interesting questions relating to combinatorial topology.

In this talk, we will talk about knotoids (introduced by Turaev) that provide us a new diagrammatic theory that is an extension of classical knot theory. Problem of classifying knotoids lies at the center of the theory of knotoids. We will construct a Laurent polynomial with integer coefficients for knotoids called the affine index polynomial and we will show how it contributes to the classification problem.