Meltem GÜLLÜSAÇ, Dokuz Eylül University.**Date:** 6th of March, 2020, Friday, **Time:** 10.30 – 12.00.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** The aim of this talk is to introduce pure injective modules and some decomposition problems related to pure injectivity.

# arithmetic

## Unit Fractions

**Haydar Göral****,** Dokuz Eylül University.**Date:** 28/02/2020, Friday, Time: 10:30.**Place:** Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B256.**Abstract:** In this talk, we will talk on unit fractions, filters and non-standard analysis.

## Hales-Jewett Theorem

Sedef Taşkın (DEU)

Date and Time: 21/02/2020, 10:30

Place: B256

**Abstract:** In this talk, we introduce the Hales-Jewett Theorem and its density version. As implications of this theorem, we will prove van der Waerden’s theorem and Szemeredi’s theorem.

## 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.

## 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.

## 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.

## 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.

## Arithmetica Izmir 3

**Place: **Dokuz Eylül University, Mathematics Department, B256

**Date:** 8 November 2019

Our workshop is supported by TMD (MAD). We are grateful to them for this support.

**Invited speakers**

Ahmet Muhtar Güloğlu, İ. D. Bilkent Üniversitesi

Faruk Temur, İzmir Yüksek Teknoloji Enstitüsü

Emrah Sercan Yılmaz, Boğaziçi Üniversitesi

**Program**

10:00—10:30: Welcome coffee break

10:30—11:45: Faruk Temur

11:45—13:30: Lunch break

13:30—14:45: Ahmet Muhtar Güloğlu

14:45—15:15: Coffee break

15:15—16:30: Emrah Sercan Yılmaz

**Abstracts and details:**

http://math.deu.edu.tr/wp-content/uploads/2019/10/arit-izmir3-program.pdf

## Variants of the Szemeredi Theorem

Selçuk Demir (DEU)

Place: B256

Date and Time: 11/10/2019, 10:30

**Abstract:** We are going to recall the ideas leading to the Szemeredi theorem and its variations including some continuous and geometric versions. We will try to explain the analytical background when needed. In later parts we plan to go into details.