I am an associate professor in the Department of Mathematics at Bursa Technical University with an interest in algebraic topology and its applications. I did my PhD on symplectic topology under the supervision of Jarek Kedra in the Institute of Mathematics at the University of Aberdeen. I am currently working on topological robotics and discrete Morse theory. Here are the links to my MathSciNet, Google Scholar and Researchgate profiles.
My Erdős number is 4.
My Cirriculum Vitae as of December 2025.
Publications & Preprints
18. N. Ekiz Yazıcı, Nursultan Kuanyshov, A. Borat, Sequential m-contiguity distance, submitted. arXiv
17. N. Ekiz Yazıcı, Nursultan Kuanyshov, A. Borat, m-contiguity distance, submitted. arXiv
16. C. A. Ipanaque-Zapata, A. Borat, (Injective) facet-complexity between simplicial complexes, submitted. arXiv
15. N. Ekiz Yazıcı, A. Borat, Higher Contiguity Distance, Journal of Fixed Point Theory and Applications, 28:33 (2026). arXiv - pdf
14. H. Alabay, A. Borat, E. Cihangirli, E. Dirican Erdal, Higher Analogues of Discrete Topological Complexity, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Vol 118:125 (2024) arXiv - pdf
13. A. Borat, M. Pamuk, T. Vergili, Contiguity distance between simplicial maps, Turkish Journal of Mathematics, Vol 47, No 2, 664-677. arXiv - pdf
12. T. Vergili, A. Borat, Topological spaces induced by homotopic distance, Journal of Linear and Topological Algebra, Vol 11 (2022), No 2, 85-91. arXiv - pdf
11. C. Ortiz, A. Lara, J. Gonzalez, A. Borat, A randomized greedy algorithm for piecewise linear motion planning, Mathematics, Vol 9, Issue 19 (2021), 2358. arXiv - pdf
(A. Borat, Simplicial distance, preprint. arXiv (improved and merged into the above paper))
10. A. Borat, T. Vergili, Higher homotopic distance, Topological Methods in Nonlinear Analysis, Vol 57 No 2 (2021), 525-534. arXiv - pdf
9. A. Borat, Digital homotopic distance between digital functions, Applied General Topology, Vol 22 (1) (2021), 183-192. pdf
8. A. Borat, Higher dimensional simplicial complexity, New York Journal of Mathematics, 26 (2020), 1130-1144. pdf
7. T. Vergili, A. Borat, Digital Lusternik-Schnirelmann category of digital functions, Hacettepe Journal of Mathematics and Statistics, Vol 49 (4) (2020), 1414-1422. pdf
6. A. Borat, M. Grant, Directed topological complexity of spheres, Journal of Applied and Computational Topology, Vol 4, Issue 1 (2020), 3-9. arXiv - pdf
5. A. Borat, T. Vergili, Digital Lusternik-Schnirelmann category, Turkish Journal of Mathematics, Vol 42 No 4 (2018), 1845-1852. pdf
4. A. Borat, Motion Planning Algorithms for Configuration Spaces in the Higher Dimensional Case, Topological Methods in Nonlinear Analysis, Vol 47, No 2 (2016), 763-767. pdf
3. A. Borat, Symplectically Aspherical Manifolds with Nontrivial Flux Groups, Acta Mathematica Hungarica, Vol 149, Issue 2 (2016), 523-525. pdf
2. A. Borat, A Characterisation of Symplectically Aspherical Manifolds, Journal of Fixed Point Theory and Applications, Vol 17, No 3 (2015), 477-482. pdf
1. Remarks on symplectically aspherical manifolds, Ph.D. thesis, 2013. pdf
Co-authors (alphabetical order)
The Hardy and Littlewood axioms
-
When one writes to the other, it is completely indifferent whether what he writes is right or wrong.
-
When one receives a letter from the other, he is under no obligation to read it, let alone answer it.
-
Although it does not really matter if we both simultaneously think about the same detail, still it is preferable that we should not do so.
-
It is quite indifferent if one of us has not contributed the least bit to the contents of a paper under our common name.