Year: 2019

On Isoartinian and Isonoetherian Modules – 2

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Hakan Şanal, Dokuz Eylül University.
Date: 29th of May, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: We will continue the seminar with some examples of comparing right isoartinian (isonoetherian) rings and right artinian (noetherian) rings. Then, we deal with the endomorphism ring of an isosimple module.
References
[1] A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism. J. Algebra 453 (2016): 578–601.
[2] A. Facchini and Z. Nazemian, Artinian dimension and isoradical of modules. J. Algebra 484 (2017): 66–87.

On Isoartinian and Isonoetherian Modules

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Hakan Şanal, Dokuz Eylül University.
Date: 22nd of May, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In [1, 2], Facchini and Nazemian generalize the idea of Artinian and Noetherian modules by considering the chain conditions up to isomorphism. They call a module M isoartinan (resp. isonoetherian) if, for every descending (resp. ascending) chain M ≥ M1 ≥ M2 ≥ · · · (resp. M1 ≤ M2 ≤ M3 ≤ · · · ) of submodules of M , there exists an index n ≥ 1 s.t. Mn ≅Mi for every i ≥ n. Similarly, M is called isosimple if M is non-zero and every non-zero submodule of M is isomorphic to M. In this seminar, we will give some properties of these three classes of modules.
References
[1] A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism. J. Algebra 453 (2016): 578–601.
[2] A. Facchini and Z. Nazemian, Artinian dimension and isoradical of modules. J. Algebra 484 (2017): 66–87.

Conjugate Fields and Primitive Element Theorem

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Hikmet Burak Özcan, İzmir Institute of Technology.
Date: 15th of May, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this talk, first we will recall what we did in the last seminar. Then we will mention conjugate fields and we will give the proof of the primitive element theorem.

Continuation of Algebraic Number Theory

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Sedef Taşkın, Dokuz Eylül University.
Date: 8th of May, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this talk, first we will recall what we did in the last seminar about integral elements. Then we will mention integrally closed rings and give some examples. Finally we will introduce algebraic elements and algebraic extensions.

The Analytic Continuation of the Riemann Zeta function

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Sedef Taşkın (DEU)

03/05/2019, Time: 10:00

Place: B256

In his epoch-making memoir of 1860 Riemann showed that the key to the deeper investigation of the distribution of the primes lies in the study of zeta function. Riemann proved that the zeta function can be continued analytically over the whole plane and its only pole being a simple pole at s=1. In this talk, we first introduce the gamma function. After that we mention analytic continuation of the zeta function. Finally, we obtain its functional equation. 

Arithmetica İzmir 2

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Place: Dokuz Eylül University, Mathematics Department, B256

Date: 10 May 2019

Our workshop is supported by TMD (MAD). We are grateful to them for this support.

Deadline for application is 2 May 2019

Application form click

Invited speakers

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