Davetli Konuşmacılar

Yusuf Civan ( Süleyman Demirel Üniversitesi )

Başlık: A short tour in combinatorics

Özet: 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 ( Cambridge Üniversitesi )

Başlık: Water waves – Two asymptotic approaches

Özet: 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 Üniversitesi )

Başlık: Mad Vet…

Özet: 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 Üniversitesi )

Başlık: Arithmetic Progressions

Özet: 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.

Program

Konuşma Başlıkları

Özet Kitapçığı

İndirmek için tıklayınız.

Katılımcılar