Kostiantyn Drach works in the fields of dynamical systems, geometric inequalities, and topological data analysis. He is currently a postdoc at the Institute of Science and Technology Austria. Starting in September, Kostya will be an assistant professor at the Universitat de Barcelona in Spain.
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 from the V. N. Karazin Kharkiv National University, earning many distinctions on the way.
Rigidity of dynamical systems, spectral rigidity, 1-dimensional holomorphic dynamics, renormalization theory, Riemannian and convex geometry
Rigidity of Newton dynamics, (with D. Schleicher),
Advances in Mathematics, 408, 2022. [open access link]
The Dynamics of Complex Box Mappings, (with T. Clark, O. Kozlovski, S. van Strien),
Arnold Mathematical Journal, 8:319-410, 2022. [open access link]
Puzzles and the Fatou-Shishikura injection for rational Newton maps, (with R. Lodge, D. Schleicher, and M. Sowinski),
Transactions of the American Mathematical Society, 374:2753-2784, 2021. [link]
A hyperbolic view of the Seven Circles Theorem, (with R. Schwartz),
The Mathematical Intelligencer, 42:61-65, 2020.
** Watch a beautiful explanation of our proof on YouTube! ** [YouTube Link]
A sausage body is a unique solution for a reverse isoperimetric problem, (with R. Chernov and K. Tatarko),
Advances in Mathematics, 353:431-445, 2019. [pdf]
A combinatorial classification of postcritically fixed Newton maps, (with Ya. Mikulich, J. Rueckert, and D. Schleicher),
Ergodic Theory and Dynamical Systems, 39(11):2983-3014, 2019.
Archimedean toroidal maps and their minimal almost regular covers, (with Y. Haidamaka, M. Mixer, and M. Skoryk),
Ars Mathematica Contemporanea, 17(2):493-514, 2019.
Inradius estimates for convex domains in 2-dimensional Alexandrov spaces,
Analysis and Geometry in Metric Spaces, 6:165-173, 2018.
On the solution of reverse Dido's problem for convex surfaces of revolution,
Dopov. Nac. Akad. Nauk Ukr., (4):7-12, 2016.
Extreme properties of curves with bounded curvature on a sphere, (with A. Borisenko),
Journal of Dynamical and Control Systems, 21(3):311-327, 2015.
Comparison theorem for the support functions of hypersurfaces, (with A. Borisenko),
Dopov. Nats. Akad. Nauk Ukr., (3):11-16, 2015. (arXiv:1402.2691 [math.DG])
Some sharp estimates for convex hypersurfaces of pinched normal curvature,
Journal of Mathematical Physics, Analysis, Geometry, 11(2):111-122, 2015.
Minimal covers of equivelar toroidal maps, (with M. Mixer),
Ars Mathematica Contemporanea, 9(2):77-91, 2015.
Isoperimetric inequality for curves with curvature bounded below, (with A. Borisenko),
Mathematical Notes, 95(5):590-598, 2014.
About the isoperimetric property of $\lambda$-convex lunes on the Lobachevsky plane,
Dopov. Nats. Akad. Nauk Ukr., (11):11-15, 2014. (arXiv:1402.2688 [math.DG])
Closeness to spheres of hypersurfaces with normal curvature bounded below, (with A. Borisenko),
Sbornik: Mathematics, 204(11):1565-1583, 2013.
About an angle comparison theorem for closed curves, (with A. Borisenko),
Dopov. Nats. Akad. Nauk Ukr., (6):7-11, 2011.