Activity Report

01 Introduction

This report documents the founding period of the Mathematics Research Center (MRC), established in August 2025 under the Azerbaijan State Oil and Industry University (ASOIU) with the support of the Ministry of Science and Education. The period covered — August 2025 through February 2026 — saw the Center build its research team, launch a regular seminar programme, host international visitors, organise an international conference, produce research publications, and begin construction of a professional digital presence.

Within six months of its founding, MRC had already established itself as a functioning international research centre, with researchers from Azerbaijan, Turkey, Ireland, and Switzerland contributing to its scientific life.

02 Research Personnel

MRC recruited its founding team of four researchers, combining established international academics with talented early-career mathematicians. All members hold doctoral degrees from leading research universities and have active international research programmes.

Founding Members

Associated Members

• ADA Univ.
  Ruslan Müslümov Algebra — biset functors, Green biset functors, module categories

Incoming Members (Spring–Summer 2026)

03 Scientific Seminars

A regular seminar programme was launched immediately upon the Center’s founding. General seminars are open to all faculty and students of ASOIU and partner institutions; research seminars are more specialised and targeted at active researchers. All seminars are held at UFAZ or the BSU Digital Research Lab, and abstracts are published on the MRC website.

Autumn 2025

• Oct 09
  Türker Bıyıkoğlu  —  MRC, ASOIU Graph entropy, degree assortativity, and hierarchical structures in networks General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Oct 23
  Ertan Elma  —  MRC, ASOIU A Discrete Mean Value of the Riemann Zeta Function and its Derivatives General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Nov 06
  Azer Akhmedov  —  North Dakota State University, USA Tiles of Groups General Seminar  ·  MRC @ UFAZ 406  ·  10:00
• Nov 13
  Lola Thompson  —  Utrecht University, Netherlands On a conjecture of Erdős, Granville, Pomerance, and Spiro General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Dec 01
  Erkko Lehtonen  —  Khalifa University, UAE The associative spectrum of a binary operation General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Dec 18
  Fırtına Küçük  —  MRC, ASOIU \(p\)-adic Artin formalism and factorization of algebraic adjoint \(p\)-adic \(L\)-functions General Seminar  ·  MRC @ UFAZ 101  ·  14:00

Spring 2026 (January–February)

• Jan 29
  Kübra Benli  —  Boğaziçi University, Türkiye Prime numbers in residue classes General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Feb 12
  Olcay Coşkun  —  MRC, ASOIU Functor of \(p\)-permutation modules General Seminar  ·  MRC @ UFAZ 101  ·  14:00
• Feb 19
  Olcay Coşkun  —  MRC, ASOIU Sorting and generating reduced words of permutations Research Seminar  ·  MRC @ UFAZ 405  ·  13:30
• Feb 26
  Olcay Coşkun  —  MRC, ASOIU From symmetries to functors: an overview of functorial representation theory General Seminar  ·  MRC @ UFAZ 203  ·  14:00

04 Scientific Output & Collaborations

Published & Accepted (2025–2026)

• 2025
  Olcay Coşkun, Alp Eden, Ersin Karabudak Revisiting a 19th Century Vector Algebra Book Journal of Humanistic Mathematics 15(2) (2025), 146–185

  Publisher
• 2025
  Fatihcan M. Atay, Türker Bıyıkoğlu Graph entropy, degree assortativity, and hierarchical structures in networks Physical Review E 112, 064315 (2025)

  Publisher
• 2025
  B. Chahal, E. Elma, N. Fellini, A. Vatwani, D. N. T. Vo On the second Hardy–Littlewood conjecture Acta Arithmetica 223 (2026) 185–196 (accepted 2025)

  Publisher
• 2026
  Olcay Coşkun & Deniz Yılmaz \(p\)-bifree biset functors Journal of Algebra (accepted 2026)

  arXiv

Preprints & Under Review

• 2025
  Olcay Coşkun & Alp Eden An Exceptional 7-dimensional Real Algebra: Octonions, \(G_2\), and the Fano Plane

  arXiv:2511.09395
• 2025
  Olcay Coşkun & Ruslan Müslümov A Categorical Decomposition of \(\mathbb{C}^\times\)-fibered \(p\)-biset Functors Subsequently accepted: Journal of Algebra 701 (2026) 779–821

  arXiv Publisher
• 2025
  İbrahim Kaan Aslan & Olcay Coşkun \(p\)-Biset Functor of Monomial Burnside Rings I: Composition Factors

  arXiv:2505.15150

Active Collaborations

• Algebra
  Olcay Coşkun & Ruslan Müslümov (ADA University) Reduced pairs for section Burnside functors
• Algebra
  Olcay Coşkun & Ergün Yalçın (Bilkent University) Relative Dade groups
• Algebra
  Olcay Coşkun & Deniz Yılmaz (Bilkent University) \(p\)-bifree functor structure of block functors
• Algebra
  Robert Boltje (UC Santa Cruz) & Olcay Coşkun The functor of \(p\)-permutation modules
• Graph Th.
  Türker Bıyıkoğlu & Mehmet Can Yavuz (Işık University) Evaluating latent space: coupling-matrix and its off-diagonals
• Number Th.
  Kazım Büyükboduk (University College Dublin) & Fırtına Küçük Algebraic adjoint \(p\)-adic \(L\)-functions around \(\theta\)-critical points of the eigencurve

05 Educational & Academic Services

Student Supervision

• PhD
  Mustafa Akdağ  —  Boğaziçi University Structure of the Monomial Burnside functor Supervisor: Olcay Coşkun
• UG Project
  Nuray İsmayilli  —  ADA University The Game of Cycles Supervisor: Türker Bıyıkoğlu

Academic Service

• Peer Review
  Journal refereeing MRC members refereed a total of 5 papers for leading international mathematics journals during this period.
• AMS
  AMS Mathematical Reviews Ertan Elma serves as an active reviewer for the American Mathematical Society’s Mathematical Reviews database.
• Outreach
  Path to Math  —  Baku student community Ertan Elma maintains regular engagement with the mathematics student community in Baku, contributing to the Path to Math club for mathematics majors.
• Internal
  Hiring & Seminar Committees All MRC members participate in the hiring committee and the seminar organisation committee.

06 Conference & International Visitors

Conference Organised by MRC

Hosted Visitors

• Nov 29–Dec 2
  Erkko Lehtonen  —  Khalifa University, UAE Research focus: universal algebra and graph algebras. Delivered a general seminar on December 1. Host: Olcay Coşkun
• Nov 12–16
  Lola Thompson  —  Utrecht University, Netherlands Research focus: analytic number theory and the Erdős–Granville–Pomerance–Spiro conjecture. Delivered a general seminar on November 13. Host: Ertan Elma
• Jan 28–29
  Kübra Benli  —  Boğaziçi University, Türkiye Research focus: prime numbers in residue classes. Delivered a general seminar on January 29. Host: Ertan Elma