Muhammed Deniz, Dokuz Eylül Univ., Department of Physics, Date: Apr 22, 2019, Monday. Time: 14:30 –16:00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206. |

# Month: April 2019

## Mathematical Physics Seminars 4- Basic Concepts and Formulations in Quantum Mechanics.

Muhammed Deniz, Dokuz Eylül Univ., Department of Physics, Date: Apr 15, 2019, Monday. Time: 14:30 –16:00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

## 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

**Program**

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

**DIFFERENTIAL EQUATIONS,****DIFFERENCE EQUATIONS,****DYNAMIC EQUATIONS,****STOCHASTIC DIFFERENTIAL EQUATIONS**

and all other fields of applied mathematics.

Workshop website: http://wdea2019.deu.edu.tr

**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)

## Mathematical Physics Seminars 3- Harmonic Oscillator Problem- Analytical Method and Free Particle.

Muhammed Deniz, Dokuz Eylül Univ., Department of Physics, Date: Apr 8, 2019, Monday. Time: 14:30 – 16:00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

## 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 .deu.edu.tr.

**Program**

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]).

**References**

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

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].

**References**

- 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.

**References**

- TSAI, Lung-Wen (1999). Robot Analysis: The Mechanics of Serial and Parallel Ma- nipulators . A Wiley-Interscience Publication
- 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.

## Mathematical Physics Seminars 2- Particle in a Box and Harmonic Oscillator Problems- Algebraic Method.

Muhammed Deniz, Dokuz Eylül Univ., Department of Physics, Date: Apr 1, 2019, Monday. Time: 14:30 – 16:00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.