Kostiantyn (Kostya) Drach does research in the fields of geometry and dynamics. He is an Assistant Professor (Professor lector) at the Universitat de Barcelona. Before that, he held several postdoc and junior positions in Austria (Institute of Science and Technology Austria), France (Aix-Marseille University), Germany (Jacobs University Bremen), and Ukraine (V.N. Karazin Kharkiv National University).
Kostya is a native of Kharkiv. After graduating from the Kharkiv Physics and Mathematics Lyceum No. 27, he obtained his bachelor's, master's, and doctoral degrees (May 2016) from the V. N. Karazin Kharkiv National University, earning many distinctions on the way.
Holomorphic dynamics
Hyperbolic dynamics and geodesic flows
Rigidity of dynamical systems
Renormalization theory
Riemannian and convex geometry
Isoperimetric inequalities
Rigidity of dynamical systems, spectral rigidity, 1-dimensional holomorphic dynamics, renormalization theory, Riemannian and convex geometry
"Wandering domains, rigidity, and root finding in holomorphic dynamics" PID2023-147252NB-I00 (AEI, Spanish Government), 2024-2027. Principal investigator (with Núria Fagella (UB)).
"Modern mathematics in Marseille and more" AMX-22-IN1-50 (A*Midex Foundation, France), 2024-2029. Co-principal investigator (with PI’s Dierk Schleicher (Aix-Marseille University/France) and Núria Fagella (UB)).
Geometria i Topologia UB, 2021SGR00697 (Generalitat de Catalunya). Member of the group.
K. Drach, L. Staresinic, S. van Strien. Density of Stable Interval Translation Maps. 2024, 75 pages, submitted. https://doi.org/10.48550/arXiv.2411.14312
K. Drach. The Blaschke rolling theorem in Riemannian manifolds of bounded curvature. 2024, 20 pages, submitted. https://doi.org/10.48550/arXiv.2404.02739
K. Drach, K. Tatarko. Reverse isoperimetric problems under curvature constraints, 2023, 39 pages, submitted. https://doi.org/10.48550/arXiv.2303.02294
K. Drach, D. Schleicher. Rigidity of Newton Dynamics. Adv. Math. 408 (2022) 108591. https://doi.org/10.1016/j.aim.2022.108591
T. Clark, K. Drach, O. Kozlovski, S. van Strien. The dynamics of complex box mappings. Arnold Math. Journal 8 (2022) 319-410. https://doi.org/10.1007/s40598-022-00200-7
K. Drach, R. Lodge, D. Schleicher, M. Sowinski. Puzzles and the Fatou-Shishikura injection for rational Newton maps. Trans. Amer. Math. Soc. 374 (2021), no. 4, 2753-2784. https://doi.org/10.1090/tran/8273
R. Chernov, K. Drach, K. Tatarko. A sausage body is a unique solution for a reverse isoperimetric problem. Adv. Math. 353 (2019), 431-445. https://doi.org/10.1016/j.aim.2019.07.005
K. Drach, Ya. Mikulich, J. Rückert, D. Schleicher. A combinatorial classification of postcritically fixed Newton maps. Ergod. Theor. Dyn. Syst. 39 (2019), no. 11, 2983-3014. https://doi.org/10.1017/etds.2018.2
K. Drach, R.E. Schwarz. A hyperbolic view of the Seven Circles Theorem. The Mathematical Intelligencer, 42 (2020) 61-65.
K. Drach, Y. Haidamaka, M. Mixer, M. Skoryk. Archimedean toroidal maps and their minimal almost regular covers. Ars Math. Contemp. 17 (2019), no. 2, 493-514. https://doi.org/10.26493/1855-3974.1825.64c
K. Drach. Inradius estimates for convex domains in 2-dimensional Alexandrov spaces. Anal. Geom. In Metric Spaces 6 (2018), 165-173. https://doi.org/10.1515/agms-2018-0009
Patents:
S. Glushakov, K. Drach, V. Shevtsova, I. Kotenko, L. Polyakova, O. Leonov. Automatic selection of optimal graphs with robust geometric properties in graph-based discovery of geometry of clinical data. US Patent Application US20240047022A1, 2024.
S. Glushakov, K. Drach, V. Shevtsova, I. Kotenko, L. Polyakova. Graph-based discovery of geometry of clinical data to reveal communities of clinical trials subjects, US Patent No. 20210349914 (US11789970B2), 2023.
S. Glushakov, V. Balon, I. Kotenko, A. Rekalo, K. Drach, B. Chornomaz, V. Shevtsova. Systems and methods for topology-based clinical data mining, US Patent No. 20200105421 (US11069447B2), 2021.