My research interests are topology and geometry. 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 symplectic geometry. Here are the links to my MathSciNet, Google Scholar and Researchgate profiles.
My Erdős number is 4.
My CV as of December 2023.
For MSc and PhD supervision and funding opportunities please send your CV and research interest to ayse (dot) borat (at) btu (dot) edu (dot) tr.
Publications & Preprints
15. N. Ekiz Yazıcı, A. Borat, Higher Contiguity Distance, submitted. arXiv
14. H. Alabay, A. Borat, E. Cihangirli, E. Dirican Erdal, Higher Analogues of Discrete Topological Complexity, submitted. arXiv
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:
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When one writes to the other, it is completely indifferent whether what he writes is right or wrong.
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When one receives a letter from the other, he is under no obligation to read it, let alone answer it.
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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.
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It is quite indifferent if one of us has not contributed the least bit to the contents of a paper under our common name.