**Haydar Göral****,** Dokuz Eylül University.**Date:** 25th of December, 2019, Wednesday, Time: 14.45 – 16.15.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** In this talk, we consider algebraic unit fractions. We show that the finiteness of the set of all solutions of certain Diophantine equations in algebraic unit fractions determines the field of rational numbers among all real number fields.

# Year: 2019

## Hales-Jewett Theorem and Some Applications

Sedef Taşkın (DEU)

Date and Time: 27/12/2019, 13:30

Place: B256

**Abstract:** In this talk, we introduce the Hales-Jewett Theorem (HJT) which is one of the cornerstones of Ramsey Theory. As implications of this theorem, we will prove the van der Waerden’s theorem and the Gallai-Witt’s theorem. We talk about some generalizations of the HJT.

## On the Strong Degrees of Unital Rings

**M. Pınar Eroğl****u**, Dokuz Eylül University.**Date:** 18th of December, 2019, Wednesday, Time: 14.45 – 16.15.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** In this seminar, we will first investigate the relationships between the degree of algebraicity of an element and its strong degree. And then we will continue to talk about the strong degrees of unital rings.

## A survey on multiplicative number theory

Haydar Göral (DEU)

Date: 13/12/2019, Time: 13:30

Place: B256

Abstract: We will survey the main results of multiplicative number theory starting from Euler and Dirichlet to the recent past.

## Multiple Zeta Values

Burak Turfan, Dokuz Eylül University.**Date:** 11th of December, 2019, Wednesday, Time: 14.45 – 16.15.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** In this talk, I will introduce Riemann zeta function and multiple zeta values. Also, We see that Euler’s formula that is values of Riemann zeta functions at the even integers. I will try to find some linear relation between Rieman zeta function and multiple zeta values. The main purpose of this talk finding algebraic relation of Q-vector spaces of R which is generated by multiple zeta values according to their weight and length, and talking about their dimensions. Finally, I will mention about some conjectures.

## Frobenius Algebras, Gendo-Symmetric Algebras, Comultiplications and Dominant Dimension

Çiğdem Yırtıcı, University of Stuttgart.**Date:** 4th of December, 2019, Wednesday, Time: 14.45 – 16.15.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** Two large classes of algebras, Frobenius algebras and gendo-symmetric algebras, are characterized by comultiplication with some special properties. But, there are differences between them. The aim of this talk is to introduce the class of gendo-symmetric algebras which is constructed by Fang and König and clarify these differences.

## Prime Ideal Theorem

Hikmet Burak Özcan

06/12/2019, Time: 13:30

Place: B256

Abstract: In this talk, firstly we will introduce the notion of number fields and we will mention the ring of integers for a given number field. Then, we will talk about the Prime Ideal Theorem, which is the number field generalization of the prime number theorem. It was proved by Edmund Landau in 1903. This theorem provides an asymptotic formula for the prime ideal counting function, which counts the number of prime ideals in the ring of integers of K with norm at most n.

## On the Strong Degree

**M. Pınar Eroğl****u**, Dokuz Eylül University.**Date:** 27th of November, 2019, Wednesday, Time: 14.45 – 16.15.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** In this seminar, we will continue to talk about the strong degree of unital rings.

## Multiple Zeta Values

Burak Turfan (DEU)

Place: **B256**

Date: 29/11/2019, Time: 13:30

**Abstract**: In this talk, I will introduce the Riemann zeta function and multiple zeta values. Then, I will show some identities between the Riemann zeta function and harmonic sums. Also, we prove Euler’s formula. I will find some linear relations between the Riemann zeta function and multiple zeta values.

## Variants of the Szemeredi Theorem – 2

Selçuk Demir (DEU)

Place: B256

Date and Time: 15/11/2019, 13:15

**Abstract:** We sill start talking about geometric versions of the Szemeredi theorem.In particular, we plan to discuss the version of the Katznelson-Weiss theorem due to Bourgain. The Katznelson-Weiss theorem says that if A is a subset of the plane with positive upper density, then for every m large enough, there are points x and y of A such that the distance between x and y is equal to m. The necessary background from harmonic analysis will be recalled.