algebra

Minimal Generating Sets Of Modules

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Mücahit Bozkurt, Manisa Celal Bayar University. Date: 9th of  October, 2024, Wednesday, Time: 13:30 – 14:30. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Office B214 (Online-Sakai-Graduate Meetings).

Abstract:  For a right R-module M, a subset X of M is said to be a generating set of M if M=\sum_{x \in X}xR; and a minimal generating set of M is any generating set Y of M such that no proper subset of Y can generate M.

In this seminar, we present some basic results concerning minimal generating sets of modules.

References

  1. Ercolanoni, S., & Facchini, A. (2021). Projective covers over local rings. Annali di Matematica Pura ed Applicata (1923-), 200(6), 2631-2644.
  2. Hrbek, M., & Růžička, P. (2017). Regularly weakly based modules over right perfect rings and Dedekind domains. Czechoslovak Mathematical Journal, 67, 367-377.
  3. Hrbek, M., & Růžička, P. (2014). Weakly based modules over Dedekind domains. Journal of Algebra, 399, 251-268.

Dreams That Touch the Sky

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Salih AKIN, Second Pilot at THY (graduated from DEU, Faculty of Science, Department of Mathematics)

Saadet SARICA, THY Cargo Marketing Directorate, Fare Specialist at the Fare Department (graduated from DEU, Faculty of Science, Department of Mathematics)

Date: Thursday, May 23, 2024

Time: 13:30

Location: DEÜ, Faculty of Science, B block, Prof. Dr. Ömer Köse Conference Hall

Summary: In this event, we will share my business processes and career experiences in the aviation industry.

 

Hydroelastic waves propagating in ice-covered channel

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Prof. Dr. Tatyana Khabakhpasheva, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 14:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Characteristics of linear hydroelastic waves propagating in an ice channel are investigated. The channel is of rectangular cross section with finite depth and of infinite extent. Liquid in the channel is inviscid and incompressible. The liquid flow caused by the ice deflection is potential. The ice is modeled by a thin elastic plate. The coupled hydroelastic problem is reduced to the problem of the wave profiles across the channel. The wave profiles are sought as series of normal dry modes of the plate, coefficients of which are to be determined. Dispersion relations of these hydroelastic waves, their critical speeds, and corresponding strain and stress distributions in the plate are determined. Several special cases in which boundary conditions, ice thickness distributions across the channel width, and ice plate compression were changed were investigated and compared with each other.

Coupled/decoupled linear/nonlinear responses of ice cover to external loads

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Prof. Dr. Alexander Korobkin, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 13:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Modelling response of an elastic floating plate to a body moving under the plate is discussed. The original problem is nonlinear and coupled with the plate deflection being dependent on the hydrodynamic pressure, which in turn depends on the plate deflection. It is shown that the problem can be treated as decoupled for some conditions of the body motion, which significantly simplifies the analysis. Within the decoupled model, the body motion and the hydrodynamic pressure along the plate/water interface are calculated without account for the plate deflection. Then this pressure is applied to the equations of the plate dynamics without account for the fluid response to the plate deflection. It is known that only rather small strains are allowed in ice plates, which limits the deflections of the ice and importance of the nonlinear effects. It is shown that nonlinear effects in problems of hydroelastic response of floating ice sheets can be approximately neglected in many practical situations.

On the Edge Cover Polynomial Properties of Certain Graph Families

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Prof. Dr. Feryal Alayont, Mathematics at Grand Valley State University

Date: May 16, 2024, Thursday

Time: 11:00 am

Place: B257, Faculty of Science, Dokuz Eylül University

Abstract: An edge cover of a simple graph is a subset of the edges so that each vertex is incident with at least one edge in the subset. The edge cover polynomial of a graph is the generating polynomial of the number of edge covers of the graph. Specifically, the edge cover polynomial is defined as where is the number of edge covers with edges. The edge cover polynomials of path and cycle graphs are known to have real roots, and hence have log-concave and unimodal coefficients. In this talk, we will describe how to construct other graph families whose edge cover polynomials have real roots and some whose polynomials have non-real roots, but still have log- concave and unimodal coefficients. This is joint work with Evan Henning and Can Selek.

Feryal Alayont is a Professor of Mathematics at Grand Valley State University. She received her B.S. in mathematics from Bilkent University, Turkey, and her Ph.D. in mathematics from the University of Minnesota. She was a teaching postdoctoral fellow at the University of Arizona from 2003 to 2006. Since 2006, she has been at Grand Valley State University in the Department of Mathematics, where she also served as the Mathematics Advising and Engagement Coordinator from 2016-2022. She is an active undergraduate research mentor and has mentored more than 75 students at GVSU. Her research interests include enumerative combinatorics, graph theory, ethics in mathematics, and the scholarship of teaching of mathematics.

Applications of Symplectic Supergeometries in Particle, String and Membrane Models

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Cem Yetişmişoğlu, İstanbul Technical University Postdoctoral Researcher.

Date: 30th of  April, 2024, Tuesday.

Time: 11.30 – 12.30.

Place: Zoom (https://itu-edu-tr.zoom.us/j/94090890378?pwd=RHpFc1l6MFBjcWU3ZGdidW9qcWRGUT09

Meeting ID: 940 9089 0378

Passcode: 035170.)

Abstract: In this talk we will talk about symplectic supergeometries and their applications coming from different areas of mathematical physics. In the first part, we will look at an application regarding statistical mechanical applications to systems with discrete degrees of freedom (math-ph:2311.05711). In the second part, we will talk about algebraic structure of symmetries associated with string/membrane models which are called algebroids. Moreover for string dualities one is interested in bialgebroids and their Drinfel’d doubles. These notions can naturally be studied using symplectic supergeometries (Voronov, Roytenberg). In this talk we will talk about reformulations of these structures in terms of vector bundles and calculi that we defined on them (hep-th:2312.06584).

Ultrafilters and Some of Their Applications

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Haydar Göral, İzmir Institute of Technology . Date: 26th of April, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Class B255

Abstract: In this talk, we first define ultrafilters on a non-empty set. Then, we see that there is a natural topology on the set of ultrafilters on the positive integers, and in fact this is the Stone-Cech compactification of the positive integers. Moreover, this compact space has an associative binary operation extending the addition of the positive integers. Finally, we will show how this topological semigroup is crucial for proving Ramsey theoretical results from combinatorics.

A Countable Prime Avoidance Theorem and Its Generalization to Prime Submodules

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M. R. Pournaki, Sharif University of Technology. Date: 29th of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: One of the fundamental cornerstones of commutative ring theory is the prime avoidance theorem, which states that, if \frak{p_1},\ldots,\frak{p_n} are prime ideals of R and \frak{a} is an ideal of R such that \frak{a}\subseteq {\bigcup_{i=1}^n} \frak{p_i}, then \frak{a}\subseteq \frak{p_i} for some 1\leq i\leq n. In this talk, we give a proof for the countable version of this theorem due to Sharp and Vamos. The proof uses the celebrated Baire’s category theorem in metric spaces. We then discuss its generalization to the prime submodules.

A Glimpse to the Stanley Depth: A Geometric Invariant for Modules

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M. R. Pournaki, Sharif University of Technology. Date: 22nd of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: Stanley depth is a geometric invariant of a module which has some common properties with the homological depth invariant. In this talk, we first review briefly the basic concepts of Stanley depth and then discuss some of the recent developments in the theory.

 

 

 

A Glimpse to Unit Graphs: The Graphs Arising From Rings

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M. R. Pournaki, Sharif University of Technology. Date: 15th of March, 2024, Friday, Time: 13.00 – 14.00. Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Classroom B255.

Abstract: The ring \mathbb{Z}_2\times\mathbb{Z}_2, having only one unit, cannot be generated by its units. It turns out, in the general theory of rings, that this is essentially the only example. In this talk, we give an elementary proof of “A finite commutative ring with nonzero identity is generated by its units if and only if it cannot have \mathbb{Z}_2\times\mathbb{Z}_2 as a quotient.” The proof uses graph theory and pointed out to the story of how unit graphs have been arisen. At the end, we discuss some of the recent developments in the theory.