Year: 2019

On the Strong Degree

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M. Pınar Eroğlu, Dokuz Eylül University.
Date: 13rd 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 introduce the concept of the strong degree of a unital ring. The definition involves a rather technical condition, but we shall see that the strong degree can be rather easily computed for certain classes of rings.

Reference: 1. Brešar, M., Chebotar, M. A., and Martindale, W. S. (2007). Functional identities. Springer Science & Business Media.

Arithmetica Izmir 3

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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

Representation Theory of Artin Algebras

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Zübeyir Türkoğlu, Dokuz Eylül University.
Date: 23rd of October, 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 talk about almost split short exact sequences. This notion is a special type of short exact sequences of modules and play a central role in the representation theory of Artin algebras.


Infinite Power of Ideals in Abelian Categories

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Sinem Odabaşı, Institute of Physics and Mathematics, Science Faculty, The Universidad Austral de Chile (UACh).
Date: 23rd of July, 2019, Tuesday. Time: 11:15 – 12:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: The ‘Phantom phenomenon’ has been sucessufelly carried into abelian setting firstly in [Her07], later in [FGHT13]. In this talk, we claim to introduce ‘ghost phenomenon’ in abelian setting which is also compatible with the existent ones in certain tringulated categories as mentioned above. Besides, we observe that the problem of being zero a finite power of ghost ideal in these triangulated categories is strongly related to being a certain type of object ideals and cotorsion pairs. Using this observation and certain techniques/results on cotorsion pairs, now we are able to ensure that under mild conditions the ideal ‘Ghost’ in an abelian category is always turned out to be ‘zero’ in some infinite power. We then apply this formalism to the ideal Ghost of chain morphisms which induce zero in homology in the category of chain complexes of left R-modules.
This is a joint work-in-progress with Sergio Estrada, X.H. Fu and Ivo Herzog, which has been supported by the grant CONICYT/FONDECYT/Iniciaci\’on/11170394.
References:
[FGHT13] Fu, X. H., Guil Asensio, P. A, Herzog, I. & Torecillas, B. (2013). Ideal approximation theory. Adv. Math. 244, 750-790.
[Her07] Herzog, I. (2007). The phantom cover of a module. Adv. Math. 215, 220–249.

İzmir Mathematics Days – II

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İzmir Mathematics Days – II September 12-13, 2019

İMD 2019

Workshop webpage: http://img.deu.edu.tr/en/

One of two aims of İzmir Mathematics Days is to provide a platform for graduate students to share their work, ideas and experiences and to build research and mentoring networks. The other one is to encourage undergraduate math majors to pursue a career in Mathematics.

In the morning sessions, four colloquium talks will be given by the invited speakers to introduce their research of interests. The afternoon sessions are devoted to graduate students and young researchers. All students are welcome to apply. There will also be an informative panel of faculty members describing the graduate program at DEU followed by Q&A session.

All abstracts must be submitted in English. The talk can be either English or Turkish but this must be clearly stated in the submission process.

Invited Speakers 

Yusuf Civan ( Süleyman Demirel University )

Title:  A short tour in combinatorics

Abstract: This is an invitatory talk to a short trip through the jungle of combinatorics, one of the fascinating fields of modern mathematics. If time permits, we plan to visit various sites in the jungle, including those from combinatorial number theory to discrete geometry, graph theory to combinatorial commutative algebra, etc. Lastly, after showing our respect to the founder king “Paul Erdös” of the jungle, we review the current status of some of his favorite open problems.

Konstantinos Kalimeris ( University of Cambridge )

Title: Water waves – Two asymptotic approaches

Abstract: TBA

Müge Kanuni Er ( Düzce University )

Title: Mad Vet…

Abstract: How does a recreational problem “Mad Vet” links to interesting and interdisciplinary mathematical research “Leavitt path algebras” in algebra and “Graph C*-algebras” in analysis. 

We will give a survey of the last 15 years of research done in a particular example of non-commutative rings flourishing from the fact that free modules over some non-commutative rings can have two bases with different cardinality.   Surprisingly enough not only non-commutative ring theorists, but also C*-algebraists gather together to advance the work done. The interplay between the topics stimulate interest and many proof techniques and tools are used from symbolic dynamics, ergodic theory, homology, K-theory and functional analysis. Many papers have been published on this structure, so called Leavitt path algebras, which is constructed on a directed graph. 

Haydar Göral ( Dokuz Eylül University )

Title: Arithmetic Progressions

Abstract: A sequence whose consecutive terms have the same difference is called an arithmetic progression. For example, even integers form an infinite arithmetic progression. An arithmetic progression can also be finite. For instance, 5, 9, 13, 17 is an arithmetic progression of length 4. Finding long arithmetic progressions in certain subsets of integers is at the centre of mathematics in the last century. In his seminal work, Szemerédi (1975) proved that if A is a subset of positive integers with positive upper density, then A contains arbitrarily long arithmetic progressions. With this result, Szemerédi proved the long standing conjecture of Erdős and Turan. Another recent remarkable result was obtained by Green and Tao in 2005: The set of prime numbers contains arbitrarily long arithmetic progressions. In this talk, we will survey these results and some ideas behind them.