Geçmiş Sunumlar

Deli Baytar senaryoları ve Çizge Teorisi

Konuşmacı: Zehra Akın- Tev İnanç Türkeş Lisesi

Tarih: 29.12.2022

Özet / Abstract

Matematik problemleri olarak ortaya çıkan Deli Baytar senaryoları arkasında cebirsel ilişkiler barındırmaktadır. Bu ilişkiler çizge teorisi yardımıyla da gösterilebilmektedir. Deli Baytar problemlerini bulmaca olarak çözmeye başlayarak çizge üzerinde göstermeyi öğreneceğiz.

Quasi-Baer *-ring characterization of Leavitt path algebras

Konuşmacı: Morteza Ahmadi- Tarbiat Modares University

Tarih: 26.10.2022

Özet / Abstract

A ring is said to be a quasi-Baer *-ring if the right annihilator of every ideal is generated by a projection. In this talk, I will introduce the notion of graded quasi-Baer *-ring. Then, I will provide the characterizations of quasi-Baer * and graded quasi-Baer * Leavitt path algebras.

On higher commutators

Konuşmacı: M. Pınar Eroğlu- Dokuz Eylül Üniversitesi

Tarih: 19.10.2022

Özet / Abstract

A general result on higher commutators due to Herstein I.N. states that if A is a noncommutative simple algebra over a field of characteristic not 2, then the only higher commutators of A are A and [A,A]. For a more general approach, the question that arises naturally is: Which assumptions should be required to obtain a result similar to above in the case where A is an arbitrary noncommutative unital algebra? In this talk, we characterize higher commutators of unital algebras discussing the question above.

Kompleks Ağlar ve Ağ Bilimi

Konuşmacı: Mehmet Şimşek - Düzce Üniversitesi

Tarih: 14.04.2022

Özet / Abstract

Ana Başlıklar:

- Kompleks Sistemler

- Graf Teorisi ve Ağ Bilimi İlişkisi

- Graflar ve Kompleks Ağlar

- Ağ Sınıfları: Düzenli Ağlar, Rasgele Ağlar, Küçük Dünya Ağları, Ölçek Bağımsız Ağlar

- Kompleks Ağlardaki Belli Başlı Çalışma Alanları: Topluluklar, Ağ Dayanıklılığı ve Direnci, Salgın Modelleme, Merkeziyet Ölçütleri

Graphs, Simplicial Complexes and Polynomial Rings

Konuşmacı: Alper Ülker - İstanbul Kültür University

Tarih: 28.03.2022

Özet / Abstract

Invertible and Locally Invertible Bases for Leavitt Path Algebras

Konuşmacı: Daniel Bossaller - Baylor University

Tarih: 26.01.2022

Özet / Abstract

Various recent papers deal with the family of so called ``invertible algebras," those algebras over arbitrary (not necessarily commutative) unital rings which have bases that consist solely of invertible elements. Many familiar algebras satisfy this property, including all finite dimension algebras over fields other than $\mathbb{F}_2$ and all $n \times n$ matrix algebras over unital rings. L\'opez-Permouth and Pilewski gave a complete characterization of precisely which Leavitt path algebras of finite graphs are invertible. In this talk I will introduce the concept of a locally invertible algebra, that is, an algebra $A$ having basis $\mathcal{B}$ such that for every $b \in \mathcal{B}$, there exists some idempotent $e$ for which $b$ is invertible in the corner algebra $eAe$. We will show that this definition is equivalent to the algebra having a basis consisting solely of strongly regular elements, and then we will give various examples and non-examples of locally invertible algebras. Afterwards we will examine local invertibility in the context of Leavitt path algebras, in particular giving a complete characterization of strongly regular monomials and, as a corollary, showing that all von Neumann regular and all directly finite Leavitt path algebras are locally invertible.

Isolated Points on Modular Curves

Konuşmacı: Özlem Ejder- Boğaziçi University

Tarih: 17.01.2022

Özet / Abstract

One of the oldest areas of mathematics is the study of integer or rational solutions to polynomial equations with integer coefficients and it remains active till today. The most natural question we can ask about such an equation is whether its set of rational solutions is finite or infinite. This can be determined by the genus of the curve defined by such equations. In particular, if the genus is greater than one, there are finitely many rational points on a curve.

What happens when one allows for solutions involving square-roots of integers or cubic roots? Perhaps in general all complex numbers that are roots of a degree d polynomial? We call such solutions of degree 2,3 or d in general. In this talk, we will discuss when a curve has infinitely many degree d points focusing particularly on points on modular curves.

Endomorphism rings and Baer - Kaplansky classes

Konuşmacı: Gabriella D’este - University of Milano

Tarih: 29.11.2021

Özet / Abstract

In the first part of my talk I will recall some facts about the so called "realization theorems" of abstract or topological endomorphism rings of abelian groups or modules. . In the second part of my talk I will present some results, contained in a joint paper with Derya Keskin Tutuncu and Rachid Tribak and in some work in progress, concerning Baer - Kaplansky classes of modules. These classes have the property that two of their modules are isomorphic if and only if their endomorphism rings are isomorphic as rings. Some of these classes have the stronger property that two of their modules are isomorphic if and only if their endomorphism rings are isomorphic as abelian groups or as vector spaces over some field.

Sonlu Cisimler Üzerinde Birçok Rasyonel Noktası Olan Drinfeld Modüler Eğrileri

Konuşmacı: Vural Cam -Selçuk Üniversitesi

Tarih: 22.11.2021

Özet / Abstract

Mathematics and Music

Konuşmacı: Alp Bassa -Boğaziçi University

Tarih: 15.11.2021

Özet / Abstract

This will be a general (math) audience talk, aiming to show some interesting number theory emerging in music theory.

Locally finite dimensional representations over Noetherian (Hopf) algebras

Konuşmacı: Can Hatipoğlu - The American University of the Middle East

Tarih: 08.11.2021

Özet / Abstract

After Eckmann and Schopf described the injective hull of a module in 1953, Matlis showed that the injective hull of a simple module over a commutative Noetherian ring is Artinian, a property which is not shared by noncommutative Noetherian rings. This finiteness condition attracted some interest over the years, particularly for its connection to Jacobson’s Conjecture. I will talk about a related finiteness condition which asks, for a Noetherian algebra $A$ over a field $k$, whether finitely generated essential extensions of finite dimensional $A$-modules are again finite dimensional. Classical examples of such algebras are enveloping algebras of finite dimensional solvable Lie algebras and group rings of polycyclic-by-finite groups, due to the works of Donkin, Dahlberg, and Feldvoss.

I will first set the scene by talking very briefly about Hopf algebras and injective modules in general. Then I will give a characterization of Noetherian algebras which satisfy this finiteness condition and provide some sufficient conditions, using the ideal theory of these algebras. I will then consider this problem for Ore extensions of an algebra $A$, which are noncommutative polynomial rings in one variable such that the coefficients and the variable commute up to an automorphism and a derivation of the algebra $A$. If time permits, I will talk about Hopf algebras which satisfy this finiteness condition, such as Ore extensions of commutative Noetherian Hopf algebras, certain Hopf crossed products, and affine Hopf algebra domains of Gelfand-Kirillov dimension less than or equal to 2 with a mild homological condition.

The talk is based on a joint work with Christian Lomp from the University of Porto.

REEL SİMETRİK OLMAYAN MATRİSLERİN ÖZDEĞERİNİN D-NJLA VE NJLA İLE HESABI

Konuşmacı: Meltem Turan - Ege University

Tarih: 13.10.2021

Özet / Abstract

Modern bilgisayarların gelişmesi büyük boyutlu simetrik olmayan matrislerin özdeğerlerinin hesaplanmasına olanak sağlamıştır. Büyük boyutlu simetrik olmayan matrisler ise çok sayıda birbirine neredeyse eşit özdeğerlere veya birbiri arasındaki açının oldukça küçük olduğu özvektörlere sahip olabilmektedir. Fakat bilinen klasik bazı Jacobi-benzeri algoritmalar bu tür matrisler için oldukça yavaş (neredeyse durağan) yakınsamaktadır. Bu sorunu aşacak simetrik olmayan matrislerin özdeğer hesabı için iki Jacobi-benzeri algoritmadan (D-NJLA ve NJLA) bahsedilecektir. Algoritmaların asimptotik kuadratik yakınsaklığının ispatı da verilecek olup neredeyse eşit çok sayıda özdeğeri olan büyük boyutlu matris örnekleri için asimptotik kuadratik yakınsadığı gösterilecektir.

Spin(7) structure with 2-plane field

Konuşmacı: Eyüp Yalçınkaya - TÜBİTAK

Tarih: 12.08.2021

Özet / Abstract

Partial Subadditivity of Tsallis Entropy

Konuşmacı: Ayça İleri-Dokuz Eylül University

Tarih: 05.08.2021

Özet / Abstract

Group codes: an application of group algebras to coding theory

Konuşmacı: Fatma Altunbulak Aksu-Mimar Sinan Fine Arts University

Tarih: 29.07.2021

Özet / Abstract

A brief introduction to Representation Theory

Konuşmacı: Victor Blasco Jimenez - Universidad de Zaragoza

Tarih: 15.07.2021

Özet / Abstract

We could say, in some sense, that groups are the most simple algebraic objects . We often study groups as abstract notions, but viewing or "representing" them as groups of symmetries of other structures helps us to understand in a better way both the structure and the group itself. A particularly important case is when our structure is some vector space. Representation theory, in its basics, deals with how groups act on vector spaces.

In this talk, we will introduce this theory in a very simple setting, and explain some of the fundamental structural results such as Maschke's Theorem. Finally, we will see how Representation Theory of finite groups can be studied in a more general setting while dealing with K-algebras and modules over them.

From applied algebra and geometry: optimization, statistics, and mathematical physics

Konuşmacı: Türkü Özlüm Çelik-Simon Fraser University

Tarih: 20.05.2021-01.07.2021

Özet / Abstract

Recent advances in both theoretical mathematics and efficient mathematical software have stimulated the use of algebra and geometry in problems arising from the sciences. In this framework, the first part of the talk will be a discussion about the Wasserstein distance of data distribution to a fixed model that is defined by polynomials. Computing this quantity means solving a non-convex optimization problem. Consequently, this part will focus on solution strategies, using methods from algebra, geometry and combinatorics. The second part aims to make a rapid excursion into the study of integrable systems through the lens of computational algebraic geometry. Specifically, the emphasis will be on exploiting tools from algebra, geometry and combinatorics to investigate solutions of the differential equations.

Arithmetic Progressions

Konuşmacı: Haydar Göral- İzmir Yüksek Teknoloji Enstitüsü (İYTE)

Tarih: 14.04.2021

Özet / 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, 11, 17, 23, 29 is an arithmetic progression of length 5. 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. Then in 2005, Green and Tao showed that the set of prime numbers contains arbitrarily long arithmetic progressions. In this talk, we survey these results.

On some aspects of uncountable ergodic theory

Konuşmacı: Asgar Jamneshan- Koç Üniversitesi

Tarih: 30.03.2021

Özet / Abstract

The talk aims at providing an introduction into some basic problems occurring in the ergodic theory of uncountable group actions and a setup and a few tools on how to resolve these issues. This part of the talk shall be accessible to anyone with a basic background in probability and analysis. Towards the end of the talk some actual results in uncountable ergodic theory will be presented. Most results will be drawn from recent preprints joint with T. Tao and other work in the area of multiple recurrence joint with P. Durcik, R. Greenfield, A. Iseli, and J. Madrid.

Bi-cocycle double-cross constructions

Konuşmacı: Serkan Sütlü- Işık Üniversitesi

Tarih: 23.03.2021

Özet / Abstract

Two well-known extension theories of Lie groups (resp. Lie algebras) are the 2-cocycle extensions, and the double-cross products (resp. double-cross sums). The former enables to decompose a Lie group (resp. a Lie algebra) into a manifold and a subgroup (resp. a vector space and a Lie sub-algebra), while the former theory allows to decompose a Lie group (resp. a Lie algebra) into two subgroups (resp. two Lie sub-algebras). We shall, in the talk, present a new extension theory associated to (twisted) cocycles, allowing to decompose a Lie group (resp. Lie algebra) into two manifolds (resp. two vector spaces), and furthermore unifying both the 2-cocycle extensions and the double-cross products/sums. Joint work with O. Esen (Gebze Tech. Univ.), and P. Guha (Khalifa Univ.).

Incidence Algebras II

Konuşmacı: Müge Kanuni Er- Düzce Üniversitesi

Tarih: 10.03.2021

Leavitt Path Algebras appearing in categorification attempts

Konuşmacı: Can Ozan Oğuz-University of Southern California

Tarih: 03.03.2021

Özet / Abstract

First conceived as a way to increase the dimension of algebraic structures in topological quantum field theories by Crane and Frenkel in 1994, categorification has become a main research focus where various techniques of enriching classical theories are being introduced. We will try to give an overview of this area and will focus on a special case, where one runs into Leavitt Path Algebras as morphism spaces in one of the candidate categories for categorifying Z[1/2] in the work in Khovanov and Tian.

Incidence Algebras I

Konuşmacı: Müge Kanuni Er- Düzce Üniversitesi

Tarih: 24.02.2021

Özet / Abstract

In his celebrated paper of 1964, "On the foundations of combinatorial theory I: Theory of Möbius Functions" Gian-Carlo Rota defined an incidence algebra as a tool for solving combinatorial problems. Incidence algebra is a specific ring of functions defined on the ordered pairs of a given partially ordered set to a given ring, moreover incidence ring is equipped with a module action by this ring. Möbius function is an element of an incidence algebra, besides with the appropriate choice of the partially ordered set, Möbius function of this incidence algebra coincides with the well-known Möbius function of number theory. A product of copies of a ring and upper triangular matrices are typical examples of incidence algebras. In the following papers of Rota with his co-authors, and papers of other contemporary authors incidence algebras are investigated as an algebraic object, as a tool in algebraic topology. After a general view of the above research, we mention the dense ideals and the maximal ring of quotients of incidence algebras.

Purity in Layman's Terms

Konuşmacı: Noyan Er - Dokuz Eylül Üniversitesi

Tarih: 17.02.2021

Özet / Abstract

This will be a repeat of the talk I gave at the Yeditepe University seminar. The target audience is mainly graduate students of algebra whom I would like to familiarize with the notion of purity and some thoughts it engenders; however, there might be something of interest for people from "all walks of mathematics", as its motivation can be derived from systems of linear equations.

Approximation by sub-methods of Fourier Series in some function spaces

Konuşmacı: Ahmet Hamdi Avşar - Balıkesir Üniversitesi

Tarih: 10.02.2021

Özet / Abstract

Tilting theory and Quiver mutation

Konuşmacı: Emine Yıldırım - Queen's Üniversitesi, Kingston, Kanada

Tarih: 03.02.2021

Özet / Abstract

In this survey talk, we will talk about a fundamental concept in representation theory: tilting modules. Tilting theory shows its inherent power by providing a firm foundation for cluster combinatorics in the theory of cluster algebras. One can study cluster combinatorics by studying certain quivers and their mutations. We are going to make these connections explicit by giving examples for the type A case. Our survey is based on two sources: Assem-Simson-Skowronski's book on representation theory of algebras and Reiten's survey on tilting theory and cluster algebras.

Auslander-Reiten Quivers of Type A_n

Konuşmacı: Fatma Kaynarca - Afyon Kocatepe Üniversitesi

Tarih: 06.01.2021

Özet / Abstract

The goal of representation theory is to classify the indecomposable modules and the morphisms between them. The Auslander-Reiten quiver is a first approximation of the module category. If the quiver is of finite representation type, then the Auslander-Reiten quiver provide a threefold information about the representation theory of the quiver: the indecomposable representations, the irreducible morphisms and the almost split sequences (these in turn should be thought of the building blocks of arbitrary representations, morphisms and short exact sequences, respectively). We will talk about how the Auslander-Reiten quivers of type A_n is created in different ways. We then show how to use the Auslander-Reiten quiver to compute the dimensions of Hom and Ext spaces between modules.

Auslander-Reiten Sequences and Auslander-Reiten Quivers: a visual introduction

Konuşmacı: Gabriella D’este - University of Milano

Tarih: 23.12.2020

Özet /Abstract

I will describe a direct construction of Auslander - Reiten sequences and Auslander - Reiten quivers in many examples of quivers of finite representation type. I will consider both quivers without relations

and quivers with relations. I list below the link to the written version of previous talks on Representation Theory, that is .a seminar addressed to PhD students [ 1 ] and two Colloquium type talks [ 2 ] and [ 3 ] .

[ 1 ] Quivers, representations and beyond, Mathematics Padova, Doctoral Program, Graduate Seminar "Seminario Dottorato", Booklet of the Graduate Seminar 2015 - 2016, 40 - 49 .

[ 2 ] Auslander - Reiten sequences and intuition, ESE - Salento ( published in Note di Matematica 37 , No. 2 (2017) 117 - 135 ) .

[ 3 ] Unofficial history of a joint work with Dieter Happel and of two unexpected quotations ( Conference in memoriam of Dieter Happel ( May 2013 ), Dedicated Papers, published in Rendiconti di Matematica e delle sue Applicazioni,Serie VII, 5 (2014) 103 - 118.

Fourier Analizi ve Derin Öğrenme

Konuşmacı: Elçim Elgün Kırımlı- İstanbul Üniversitesi

Tarih: 16.12.2020

Özet /Abstract

Fourier Analizi özünde (insan) gözü ve kulağının çalışmasını modeller. Derin öğrenme

ise beynin yapısından esinlenerek tasarlanmış bir makine öğrenme tekniğidir. Bu

konuşmanın amacı göz ya da kulağa gelen bir sinyal (stimuli) in anlamlandırılmasını

modellemektir.

Doğadan Esinlenen Optimizasyon Algoritmaları ve Mühendislik Problemlerine Çözümleri

Konuşmacı: Pakize Erdoğmuş - Düzce Üniversitesi

Tarih: 02.12.2020

Seminer Odası ve Kayıt Linki: https://3b.duzce.edu.tr/b/pak-7cp-nx2

Types and Representations of Quivers-I-II

Konuşmacı: Fatma Kaynarca - Afyon Kocatepe Üniversitesi

Tarih: 11.11.2020 / 18.11.2020

Özet / Abstract

Quiverler ve onların temsilleri, sonlu boyutlu cebirlerin temsil teorisinde önemli rol oynarlar. Bunun dışında pek çok uygulama alanı bulunan quiverler, tiplerine göre sınıflandırılırlar ve bazı problemlerin çözümlerinde kullanılırlar. Öncelikle quiver kavramı ve quiver tiplerinden söz edilecektir. Daha sonra quiver temsili kavramı tanıtılarak bazı örnekler verilecektir. Ayrıca quiver temsilleri ile modül kategorileri arasındaki ilişkiden söz edilecektir.

Yöneylem Araştırması

Konuşmacı: Ayten Koç - Gebze Teknik Üniversitesi

Tarih: 04.11.2020

Özet / Abstract

Yöneylem araştırmasının tarihçesinden ve temel kavramlarından bahsedilecek olup bazı yöneylem araştırması problemleri verilecektir.

Fermat's Last Theorem

Konuşmacı: Victor Blasco Jimenez - Universidad de Zaragoza

Tarih: 12.06.2020

Özet / Abstract

Fermat's Last Theorem is one of the most famous theorems of all time. Classically, the problem has been divided into different cases depending on the prime exponent of the equation x^p+y^p+z^p=0. In this talk we will overview and introduce the necessary algebraic concepts to prove the following: Let p be a regular prime. Then the equation x^p+y^p+z^p=0 does not have any non-trivial integral solution if p does not divide xyz.

Königsberg Köprüsü

Konuşmacı: Arzu Erbek - Celal Bayar Üniversitesi

Tarih: 24.04.2020

Özet / Abstract

Bu konuşmada, Leonhard Euler in 1741 yılında yayınlanan içinde uzaklık ve ölçü kavramları olmayan sadece konumlarla yeni bir geometriden söz ettiği makalesinden bahsedilecektir.

Evolution Algebras and Graphs

Konuşmacı: Vural Cam - Selçuk Üniversitesi

Tarih: 10.04.2020-17.04.2020

Özet / Abstract

This talk entirely goes over the paper "Evolution Algebras and Graphs" written by Alberto Elduque and Alicia Labra. In this paper, they explained that nilpotency of an evolution algebra equivalent to the nonexistence of oriented cycles in the corresponding graph. Moreover, they showed that the automorphism group of any evolution algebra E with E^2=E is always finite.

Yönlü Çizgelerin Döngüsüzlük Komplekslerinin Topolojisi, Renklendirme ve Döngü-kıran Sayıları

Konuşmacı: Zakir Deniz - Düzce Üniversitesi

Tarih: 06.03.2020 / 13.03.2020

Özet / Abstract

Bu konuşmada yönlendirilmiş tam çizgelerin (tournament) döngüsüzlük komplekslerinin homotopi yapıları belirlenerek çizgenin kromatik sayısı ve döngü-kıran sayısı gibi kombinatoryal parametreleri ile arasındaki ilişkiye yer verilmiştir.

Border Bases

Konuşmacı: Bilge Şipal - İstanbul Kültür Üniversitesi

Tarih: 21.02.2020 / 28.02.2020

Özet / Abstract