September 12-13, 2019

One of two aims of İzmir Mathematics Days is to provide a platform for graduate students to share their works, 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 in English or in Turkish but this must be clearly stated in the submission process.

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: Asymptotic methods have a long and illustrious history in a plethora of categories both in pure and applied mathematics. The theoretical tools of asymptotic analysis provide the appropriate background for the development of methods for studying problems originated from the real world; furthermore, these methods find several applications in hysical problems.

In this talk we emphasise their application to partial differential equations which model certain problems of fluid dynamics. First, we use techniques from asymptotic analysis and perturbation theory to obtain approximate analytical and numerical solutions of a non-linear boundary value problem which comes from the Euler’s equations for fluids and describes two dimensional water waves travelling at constant speed. Second, we derive a non-local formulation for a more general modelling of water waves, including waves with moving boundaries which are related with the study of tsunamis; we present analytical and computational results that the above techniques produce for particular cases of this problem.

** **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.