Research & Publications

RESEARCH & PUBLICATIONS

My work concerns exact methods in theoretical and mathematical physics. I am particularly interested in the connections between supersymmetric gauge theories, integrable models and special functions.

INSPIRE · Google Scholar · ORCID

Research directions

Supersymmetric gauge theories

Partition functions and supersymmetric indices make it possible to compare dual descriptions of quantum field theories. I study these exact quantities and use Bailey-type constructions to generate new families of identities and dualities.

Integrability & special functions

I work on Yang–Baxter equations, star–triangle and pentagon relations, and hypergeometric sums and integrals. These problems connect solvable statistical models with the algebraic structures behind supersymmetric dualities.

Hamiltonian systems

My interests include Lagrangian and Hamiltonian formulations of nonlinear equations, constrained dynamics and soliton equations. Recent work addresses supersymmetric extensions and the Dirac–Bergmann analysis of constraints.

String field theory & topology

I am also interested in analytic solutions of open string field theory and in relations between supersymmetric indices, triangulated three-manifolds and knot theory.

Selected papers and preprints

The selection below is arranged by year. Each arXiv link gives the paper, its version history and bibliographic record. The profiles above provide a broader publication list.

2026

Inverse scattering method for nonlinear negative first order coupled Klein-Gordon equation

Cihan Sabaz, Ilmar Gahramanov, Mansur I. Ismailov

Soliton solutions, conservation laws and the Hamiltonian structure of a coupled nonlinear system.

arXiv:2609.02844

New Beta Integral from Supersymmetric Gauge Theory on Projective Space

Ilmar Gahramanov, Tuğba Hırlı, R. Semih Kanber, Hjalmar Rosengren

A basic hypergeometric integral identity obtained from supersymmetric partition functions on RP² × S¹.

arXiv:2606.29409

Hamiltonian formulation of the supersymmetric KdV equation

Ali Pazarci, Nadir Ghazanfari, Ilmar Gahramanov

A constrained Hamiltonian description using the Dirac–Bergmann method.

arXiv:2605.08065

2025

Lens Hyperbolic Modular Double

Yağmur Bülbül, Ilmar Gahramanov, Ali Mert Yetkin, Reyhan Yumuşak

An algebraic construction whose intertwining operator yields a solution of the Yang–Baxter equation.

arXiv:2511.06400

Bailey Pairs for the Tetrahedron Index

Ilmar Gahramanov, Sinan Ulaş Öztürk, Uveys Turhan

Bailey pairs associated with the pentagon identity for the tetrahedron index.

arXiv:2510.20999

Bailey chain approach to 2d N=(0,2) dualities

Zehra Akbulut, Ilmar Gahramanov, Anıl Kahraman, Mustafa Mullahasanoglu, Yaren Yıldırım

An iterative construction of identities between elliptic genera of dual quiver gauge theories.

arXiv:2510.19713

Ising 100: review of solutions

Oğuz Alp Ağırbaş, Anıl Ata, Eren Demirci, Ilmar Gahramanov, Tuğba Hırlı, R. Semih Kanber, Ahmet Berk Kavruk, Mustafa Mullahasanoğlu, Zehra Özcan, Cansu Özdemir, Irmak Özgüç, Sinan Ulaş Öztürk, Uveys Turhan, Ali Mert T. Yetkin, Yunus Emre Yıldırım, Reyhan Yumuşak

A review of solutions of the two-dimensional Ising model, developed from our 2024 seminar series.

arXiv:2504.09661

2024