Arithmetica İzmir 2

Place: Dokuz Eylül University, Mathematics Department, B256

Date: 10 May 2019

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

Deadline for application is 2 May 2019

Application form click

Invited speakers

Ali Ulaş Özgür Kişisel, Middle East Technical University

Ayberk Zeytin, Galatasaray University

Ekin Özman, Boğaziçi University

Yıldırım Akbal, Atılım University


9:15—9:30: Opening

9:30—10:45: Ali Ulaş Özgür Kişisel

10:45—11:15: Coffee break

11:15—12:30: Ekin Özman

12:30—14:30: Öğle arası

14:30—15:45: Yıldırım Akbal

15:45—16:15: Coffee break

16:15—17:30: Ayberk Zeytin

Ali Ulaş Özgür Kişisel, Middle East Technical University

Title: Line Arrangements Over Different Base Fields 

Abstract: There are various obstructions regarding the existence of line arrangements in the projective plane over a given base field. In this talk, some of these obstructions and how they depend on the chosen base field will be explained. 

Ekin Özman, Boğaziçi University

Title: Modularity, rational points and Diophantine Equations

Abstract: Understanding solutions of Diophantine equations over rationals or more generally over any number field is one of the main problems of number theory. One of the most spectacular recent achievement in this area is the proof of Fermat’s last theorem by Wiles. By the help of the modular techniques used in this proof and its generalizations it is possible to solve other Diophantine equations too.  Understanding quadratic points on the classical modular curve or rational points on its twists play a central role in this approach. In this talk, I will summarize the modular method and mention some recent results about points on modular curves. This is joint work with Samir Siksek.

Yıldırım Akbal, Atılım University

Title: Waring’s Problem, Exponential Sums and Vinogradov’s Mean Value Theorem    

Abstract: Having introduced Hardy&Littlewood Circle method, we will jump to Waring’s Problem: representability of a large integer as the sum of s kth powers of positive integers,  which was the main motivation of Vinogradov to study a system equations (called Vinogradov’s system). Next we move on Vinogradov’s mean value theorem: a non-trivial upper-bound on the number of solutions to Vinogradov’s system, and then mention the milestone contributions of Vinogradov, Wooley and Bourgain (rip) et al.  
Last but not least, some applications of Vinogradov’s mean value theorem on exponential sums will be given. 

Ayberk Zeytin, Galatasaray University

Title: Arithmetic of Subgroups of PSL2(Z)

Abstract: The purpose of the talk is to introduce certain arithmetic questions from a combinatorial viewpoint. The fundamental object is the category of subgroups of the modular group and its generalizations. I will try to present the different nature of arithmetic of subgroups of finite and infinite index  and their relationship to classical problems. I plan to  formulate specific questions at the very end of the presentation and, if time permits, our contribution to both worlds. 
This is partly joint with M. Uludag

WDEA2019 – The 9th International Workshop on Differential Equations and Applications

It is our pleasure to invite you to participate in “The 9th International Workshop on Differential Equations and Applications” which will be organized by Department of Mathematics of both Dokuz Eylül University and Yeditepe University and held in Doğa Holiday Village, İstanbul on May 24-26, 2019. The scope of the conference is to bring together members of the mathematical community whose interest lies in applied mathematics to assess new developments, ideas and methods. The conference will cover a wide range of topics of


and all other fields of applied mathematics.

Workshop website:

Scientific Committee

Prof. Dr. Metin Gürses (Bilkent University)

Prof. Dr. A. Okay Çelebi (Yeditepe University)

Prof. Dr. Hüsnü Ata Erbay (Özyeğin University)

Prof. Dr. Varga Kalantarov (Koç University)

Prof. Dr. Maciej Blaszak (Adam Mickiewicz University)

Prof. Dr. Mieczysław Cichoń (Adam Mickiewicz University)

Prof. Dr. Wen-Xiu Ma (University of South Florida)

Prof. Dr. H. Mete Soner (Swiss Federal Institute of Technology)

Prof. Dr. Ayşe Hümeyra Bilge (Kadir Has University)

Prof. Dr. Albert Erkip (Sabancı University)

Prof. Dr. Oktay Pashaev (İzmir Institute of Technology)

Prof. Dr. İsmagil Habibullin (Russian Academy of Sciences)

Prof. Dr. Alp Eden (Boğaziçi University)

Organizing Committee

Assoc. Prof. Dr. Burcu Silindir Yantır (Dokuz Eylül University)

Asst. Prof. Dr. Meltem Adıyaman (Dokuz Eylül University)

Asst. Prof. Dr. Gülter Budakçı (Dokuz Eylül University)

Assoc. Prof. Dr. Ahmet Yantır (Yaşar University)

Assoc. Prof. Dr. Aslı Pekcan (Hacettepe University)

Workshop on Algebraic and Applied Topology

Workshop on Algebraic and Applied Topology
Dokuz Eylül University, İzmir
April 19, 2019

The goal of the workshop is to bring together the researchers from the fields of Algebraic Topology and Applied Topology in Turkey to discuss their field of interests and to initiate new collabrations for future research projects.

The morning session will be held at Room B256, Department of Mathematics and the afternoon session will be held at Room B258, Department of Mathematics. For more information, send an e-mail to asli.ilhan at


10:00-11:00 Ayşe Borat
11:00-11:20 Coffee Break
11:20-12:10 Matthew Gelvin
12:10-14:00 Lunch
14:00-14:50 Mehmet Akif Erdal
14:50-15:00 Coffee Break
15:00-15:50 Hanife Varlı
15:50-16:00 Coffee Break
16:00-16:30 Sabri Kaan Gürbüzer
16:30-16:40 Coffee Break
16:40-17:10 Derya Bayrıl Aykut

A Survey on Topological Robotics
Ayşe Borat

Topological robotics is a field initiated by Michael Farber in 2003. This new field tries to answer topological questions which are inspired by robotics and engineering. In this talk, we will give a brief survey in topological robotics mainly focusing on an important homotopy invariant called Topological Complexity which measures how far a space away from admitting a motion planning algorithm.

Euler Characteristics of Categories and Control of Homotopy Type
Matthew Gelvin

The Euler characteristic of a simplicial complex is a well-known and important combinatorial invariant. When considering small categories and their geometric realizations, one might hope that there is a similar invariant, ideally one that generalizes the classical Euler characteristic in the case of posets. Leinster defined such an object and proved some of its basic properties.

In this talk, I will outline Leinster’s notion of the Euler characteristic of a category and describe how it was used in joint work with Jesper Møller to guide our search for objects that control the homotopy type of certain categories that arise in the study of p-local finite groups.

Fibration Categories from Enrichments
Mehmet Akif Erdal

Fibration categories, as introduced by Brown [1], provide convenient models for homotopy theories as weaker alternatives to model categories. In this talk we will discuss fibration category structures that are induced by enrichments in symmetric monoidal model categories. We will also show that various categories of operator algebras, including Schocket and Uuye’s homotopy theory for $C^*$-algebras [4,5], and their equivariant versions are examples of fibration categories induced by enrichments. By using this, we recover known results that equivariant $KK$-theories and $E$-theories are triangulated categories (see [2,3]).

  1. Kenneth S. Brown. Abstract homotopy theory and generalized sheaf cohomology. Trans. Amer. Math. Soc., 186:419–458, 1973.
  2. Ralf Meyer and Ryszard Nest. The baum–connes conjecture via localisation of categories. Topology, 45(2):209–259, 2006.
  3. Ryszard Nest and Christian Voigt. Equivariant Poincar ́e duality for quantum group actions. Journal of Functional Analysis, 258(5):1466–1503, 2010.
  4. Claude Schochet. Topological methods for c-algebras. i. spectral sequences. Pacific Journal of Mathematics, 96(1):193–211, 1981.
  5. Otgonbayar Uuye. Homotopical algebra for $C^*$-algebras. Journal of Non- commutative Geometry, 7(4):981–1006, 2013.

Discrete (and Smooth) Morse Theory
Hanife Varlı

The primary concern of Morse theory is the relation between spaces and functions. The center of interest lies in how the critical points of a function defined on a space affect the topological shape of the space and conversely. Discrete Morse theory, developed by Robin Forman, is a discrete version of Morse theory that turned out to be also an efficient method to study of the topology of the discrete objects such as simplicial and cellular complexes.

In this talk, we will briefly mention smooth Morse theory, then talk about discrete Morse theory. In particular, we will talk about perfect discrete Morse functions, and the problem of composing and decomposing perfect discrete Morse functions on the connected sum of triangulated manifolds.

On a Decomposition of the Bicomplex of Planar Binary Trees
Sabri Kaan Gürbüzer

In this talk, we will introduce some simplicial properties of the set of planar binary trees and a decomposition of the bicomplex into vertical towers given Frabetti [1].

  1. Frabetti, A., Simplicial properties of the set of planar binary trees. Journal of Algebraic Combinatorics, 32, 41-65,(2001).

On the Lie Algebra of Spatial Kinematics
Derya Bayrıl Aykut

A spatial displacement is a composition of a spatial rotation followed by a spatial translation. There is an invariant line of these transformations, called screw axis. In this talk we will mention about velocity analaysis of a general spatial motion.

  1. TSAI, Lung-Wen (1999). Robot Analysis: The Mechanics of Serial and Parallel Ma- nipulators . A Wiley-Interscience Publication
  2. Selig, J. M. (2005). Geometric Fundamentals of Robotics. Springer(USA).


The Last Call For Algebraic Number Theory

Sedef Taşkın, Dokuz Eylül University.
Date: 3rd of April, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: This talk will be a continuation of the series of talks about algebraic number theory. First we start with integral elements and mention some properties. Then we introduce algebraic elements and algebraic extensions.