Strategic Plan

01 Executive Summary

The Mathematics Research Center aims in 2026 to consolidate a core team of seven international researchers, establish a high-standard Master of Mathematics programme, and host a series of high-impact workshops. This plan details the specific research trajectories, educational initiatives, and measurable outputs designed to elevate the standing of the Republic of Azerbaijan within the global scientific community.

02 Core Research Faculty

The MRC currently consists of four active members, with two additional international researchers joining in 2026. The team consists of world-class specialists bridging the gap between local talent and global expertise.

03 Detailed Research Portfolio

Our members lead independent but globally integrated research programmes with partners in the USA, Germany, Ireland, and Turkey.

Türker Bıyıkoğlu — Graph Theory

• METU
  Inferential Reasoning in Knowledge Graphs Joint project with Aziz Zambak, Philosophy Dept, METU Ankara.
• Germany
  Novel Graph Algorithm for De Novo Sequencing Joint project with Jens Allmer, Hochschule Ruhr West, Mülheim.

Olcay Coşkun — Algebraic Structures & Biset Functors

• ADA Univ.
  Simple fibered biset functors Joint with Ruslan Müslümov.

  Determining the explicit structure of simple functors that frequently occur in applications, to be applied to finite group representation theory.
• Bilkent
  \(p\)-bifree functor structure of block functors Joint with Deniz Yılmaz.

  Applying the theory of \(p\)-biset functors to block functors to target conjectures in the field.
• UCSC
  Functor of \(p\)-permutation modules Joint with Robert Boltje.

  Determining the exact structure of the trivial source functor controlling the class of all \(p\)-permutation modules.
• Boğaziçi
  Monomial Burnside rings for \(p\)-groups Joint with Mustafa Akdağ.

  Determining indecomposable summands both as a ring and as a module to complete the explicit structural analysis.

Ertan Elma — Analytic Number Theory

• Dirichlet
  Error term in the PNT for arithmetic progressions

  Studying series where zeros come from a Dirichlet \(L\)-function. Investigating structural differences regarding exceptional zeros when character moduli differ.

Fırtına Küçük — Iwasawa Theory

• UCD
  Algebraic adjoint \(p\)-adic \(L\)-functions Joint with Kazım Büyükboduk.

  Deriving a factorization formula around \(\theta\)-critical points of the eigencurve, addressing the decomposition of local Galois representations.

04 Local & Interdisciplinary Collaboration

In line with our mission to create a vibrant local ecosystem, the MRC is actively developing partnerships to bridge pure mathematical theory with applied scientific problems.

05 Educational Activities

One of the main goals of MRC is to create a research-friendly environment in Baku. We are open to undergraduate and graduate supervision to attract future mathematicians.

• MSc
  Master of Mathematics Outline submitted to the Ministry. Target: 3 students per year.
• PhD
  PhD in Algebra curriculum Ready to lead following ASOIU announcements.
• Thesis
  Mustafa Akdağ — Boğaziçi University Structure of the Monomial Burnside functor Supervisor: Olcay Coşkun
• Undergrad
  Nuray İsmayilli — ADA University The Game of Cycles Supervisor: Türker Bıyıkoğlu

06 Scientific Output & Publications

The fundamental philosophy of the MRC is the pursuit of depth and quality over mere quantity. We prioritize substantive work in reputable journals, referencing the Australian Mathematical Society’s rankings as our benchmark. The publication cycle in top-tier mathematics journals typically exceeds ten months, necessitating a long-term strategic view of research output.

Published & Accepted (2025–2026)

• 2025
  Olcay Coşkun, Alp Eden, Ersin Karabudak Revisiting a 19th Century Vector Algebra Book Journal of Humanistic Mathematics 15(2): 146–185 (2025)
• 2025
  Fatihcan M. Atay, Türker Bıyıkoğlu Graph entropy, degree assortativity, and hierarchical structures in networks Physical Review E 112, 064315 (2025)

  Publisher
• 2025
  Bittu Chahal, Ertan Elma, Nic Fellini, Akshaa Vatwani, Do Nhat Tan Vo On the second Hardy–Littlewood conjecture Acta Arithmetica 223 (2026) 185–196

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

  arXiv:2505.16719

Preprints & Under Review

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

  arXiv:2511.09395v2
• 2026
  Olcay Coşkun, Ruslan Müslümov A Categorical Decomposition of \(\mathbb{C}^\times\)-fibered \(p\)-biset Functors

  arXiv:2505.15163 Publisher
• 2026
  İbrahim Aslan, Olcay Coşkun \(p\)-Biset Functor of Monomial Burnside Rings I: Composition Factors

  arXiv:2505.15150

07 Research Infrastructure Requirements

To maintain momentum and ensure the center functions at international standards, the following infrastructural needs must be addressed as a priority for 2026.