Ulusal Matematik Sempozyumlarının 34’üncüsü, Türk Matematik Derneğinin desteği ile Dokuz Eylül Üniversitesi Matematik Bölümünde, 31 Ağustos-3 Eylül 2022 tarihleri arasında yüzyüze gerçekleştirilecektir. 1988 yılından beri gerçekleştirilen Ulusal Matematik Sempozyumlarının programı, genel konuşma, çağrılı ana konuşmalar, dizi konuşmalar ve genç araştırmacı konuşmaları, kısa konuşmalar ve poster sunumlarından oluşmaktadır.

İzmir’in kurtuluşunun 100. yılında sizleri ağırlamaktan gurur ve mutluluk duyacağız.

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.

Due to COVID-19 pandemic, the workshop will be held ONLINE.

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

Invited Speakers

Ali Sinan Sertöz (Bilkent University)

Fatma Altunbulak Aksu (Mimar Sinan Fine Arts University)

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.

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

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

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.

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 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].

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).