The project investigates fundamental questions at the interface of quantum computing, polyhedral geometry, and topology. Broadly, we study the mathematics of quantum advantage—how and why quantum computation can outperform classical computation—and develop rigorous tools to analyze and leverage this gap. Our work spans three interconnected directions: (i) quantum computing / quantum information / quantum foundations, focusing on the structure and complexity of quantum computational models; (ii) optimization and related graph-theoretic methods, using polyhedral geometry and algorithmic optimization (e.g., vertex/facet–based techniques) to formulate and solve core computational subroutines; and (iii) algebra, topology, and category theory, which provide a unifying language for organizing these structures and guiding new mathematical and algorithmic developments. 

A Ph.D. in mathematics, physics, computer science, or a closely related area is required. 

To be considered for the initial review, with an intended start date of September 1, 2026, please submit your application by May 15, 2026. Applications will be reviewed on a rolling basis; early applications are encouraged, and an earlier start date may be possible.

To apply, please submit the following materials: 

• Cover letter (describing alignment with the project) 
•  Curriculum vitae (CV) 
•  Research statement 
•  At least three reference letters 

 For questions, please feel free to contact cihan.okay@bilkent.edu.tr.