Mathematics Research Center
Baku, Azerbaijan
Activity Report
Submitted to the Rector of ASOIU by Olcay Coşkun, Director
01 Introduction
During the first five months of 2026, the Mathematics Research Center continued and deepened the scientific programme established in its founding year. This period was marked by a vigorous seminar schedule featuring both international guests and MRC members, by the acceptance and publication of research papers in leading international journals, by the launch of the Center’s digital infrastructure, and by the continued development of collaborative projects with researchers at institutions in Turkey, Ireland, the United States, and elsewhere.
This report covers all activities from January through May 2026 and is submitted to provide the Rector with a full account of MRC’s scientific output, visitor programme, personnel, and operational developments.
02 Research Personnel
Current Members
Incoming Members
Associated Members
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ADA Univ.
Ruslan Müslümov Algebra — biset functors, Green biset functors, module categories
03 Scientific Seminars
The MRC seminar programme continued weekly throughout the period, comprising general seminars open to the wider university community and research seminars for MRC members and close collaborators. All abstracts and recordings are archived on the MRC website.
General Seminars
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Jan 29
Kübra Benli — Boğaziçi University, Türkiye Prime numbers in residue classes MRC @ UFAZ 101 · 14:00
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Feb 12
Olcay Coşkun — MRC, ASOIU Functor of \(p\)-permutation modules MRC @ UFAZ 101 · 14:00
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Feb 26
Olcay Coşkun — MRC, ASOIU From symmetries to functors: an overview of functorial representation theory MRC @ UFAZ 203 · 14:00
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Mar 12
Yagub N. Aliyev — ADA University The number of inscribed and circumscribed polygons MRC @ UFAZ 101 · 14:00
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Apr 10
Nijat Aliyev — Baku Higher Oil School Subspace method for approximation of \(H_\infty\) norms of large-scale control systems MRC @ UFAZ 101 · 14:00
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Apr 21
Ergün Yalçın — Bilkent University, Türkiye Worst-case examples for the computation of persistent homology MRC @ UFAZ 308 · 14:15
Research Seminars
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Feb 19
Olcay Coşkun Sorting and generating reduced words of permutations
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Mar 05
Ertan Elma Dirichlet L-functions I
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Apr 09
Ertan Elma Dirichlet L-functions II
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Apr 16
Türker Bıyıkoğlu Castelnuovo-Mumford regularity of graphs
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Apr 30
Olcay Coşkun Equivalences on primitive Dirichlet characters
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May 07
Fırtına Küçük Iwasawa theory for graphs
04 Scientific Output
Published & Accepted (2026)
- Apr 2026
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2026
Türker Bıyıkoğlu A Note on the TxGraffiti Conjecture about Harmonic Index and Minimum Maximal Matching Number MATCH Commun. Math. Comput. Chem. 96 (2026) 1097–1099
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2026
Olcay Coşkun & Deniz Yılmaz \(p\)-bifree biset functors Journal of Algebra (accepted 2026)
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2026
B. Chahal, E. Elma, N. Fellini, A. Vatwani, D. N. T. Vo On the second Hardy–Littlewood conjecture Acta Arithmetica 223 (2026) 185–196
Preprints & Under Review
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May 2026
İbrahim Kaan Aslan & Olcay Coşkun \(p\)-Biset Functor of Monomial Burnside Rings I: Composition Factors
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Nov 2025
Olcay Coşkun & Alp Eden An Exceptional 7-dimensional Real Algebra: Octonions, \(G_2\), and the Fano Plane
Active Collaborations
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Algebra
Olcay Coşkun & Ruslan Müslümov (ADA University) Essential algebras of shifted Burnside functors
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Algebra
Olcay Coşkun & Ergün Yalçın (Bilkent University) Relative Dade groups
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Algebra
Olcay Coşkun & Deniz Yılmaz (Bilkent University) \(p\)-bifree biset functor structure of block functors
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Algebra
Robert Boltje (UC Santa Cruz) & Olcay Coşkun The functor of \(p\)-permutation modules
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Number Th.
Türker Bıyıkoğlu & Mehmet Can Yavuz (Işık University) Evaluating latent space: coupling-matrix and its off-diagonals
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Number Th.
Kazım Büyükboduk (University College Dublin) & Fırtına Küçük Algebraic adjoint \(p\)-adic \(L\)-functions around \(\theta\)-critical points of the eigencurve
05 Educational Activities
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PhD
Mustafa Akdağ — Boğaziçi University Structure of the Monomial Burnside functor Supervisor: Olcay Coşkun
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UG Project
Nuray İsmayilli — ADA University The Game of Cycles Supervisor: Türker Bıyıkoğlu
06 International Visitors
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Apr 18–23
Ergün Yalçın — Bilkent University, Türkiye Research focus: Relative Dade groups and endotrivial modules. Delivered a general seminar on April 21. Host: Olcay Coşkun
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Jan 28–29
Kübra Benli — Boğaziçi University, Türkiye Research focus: Prime numbers, residue classes, and analytic number theory. Delivered a general seminar on January 29. Host: Ertan Elma
07 Digital Infrastructure & Website
The construction and launch of the MRC website (mrc-baku.org) was carried out in full by the Director. The site was designed from scratch as a professional research centre platform, with no use of generic themes or templates. The following provides an account of the work involved and the capabilities of the resulting platform.
A bespoke visual identity was created for MRC, consistent across all pages. The system uses a four-colour palette (cream, rust, gold, slate), two typefaces (EB Garamond for body text, DM Mono for labels and metadata), and a set of structural conventions (borders, shadows, section labels) that give the site a scholarly but contemporary appearance appropriate for an international research centre.
Every page of the site was built as a custom HTML block in WordPress, with no reliance on the default theme’s styling. The following pages are live or in active development:
The site includes several technical features beyond standard WordPress:
- MathJax integration — all seminar abstracts and publication titles render mathematical notation via LaTeX syntax in the browser.
- Automatic news feed — posts assigned to News subcategories (Publication, Seminar Abroad, New Member, Award, Milestone, Visitor) are fetched automatically from the WordPress REST API and displayed on the News page with colour-coded badges and year grouping.
- Group activity feeds — each research group page has a live activity feed that pulls from all posts tagged with that group, covering both seminar and news post types simultaneously.
- Seminar database — a fully searchable and filterable archive of all 40+ seminars held since founding, with abstracts, speakers, dates, and locations.
- Publications database — searchable and filterable by year and keyword, with separate panels for published work and preprints.
- Events sidebar — the home page shows upcoming and recent events drawn automatically from WordPress posts, with intelligent date extraction from post content.
- Email templates — standardised HTML email templates for seminar announcements, used for the MRC mailing list.
- Bilingual support — a standalone Azerbaijani-language home page (/az/) provides a full overview of MRC for Azerbaijani-speaking audiences, local institutions, and the Ministry.
- Gallery — a masonry photo gallery with category filters (Seminars, FGTR 2025, Conferences, Visitors, MRC).
- Scroll-to-top & language switcher — the site header includes a language toggle (EN/AZ) and a scroll-to-top button that appears on long pages.
We plan to migrate the site from the development domain (mrc-baku.org) to the institutional domain (mrc.asoiu.edu.az) hosted on ASOIU servers when the subdomain functions with no problems.