I study Complex Dynamics and Geometric Function Theory using quasiconformal methods. I have links to videos of some talks about the papers listed below on a different part of this website. My research is partially supported by the National Science Foundation; grant DMS-2246876.
1. Analytic and Topological Nets . Kirill Lazebnik.
2. Hilbert's Lemniscate Theorem for Rational Maps. Christopher J. Bishop, Kirill Lazebnik.
3. A Geometric Approach to Polynomial and Rational Approximation. Christopher J. Bishop, Kirill Lazebnik.
4. Transcendental Julia Sets of Minimal Hausdorff Dimension. Jack Burkart, Kirill Lazebnik.
11. Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions. Christopher J. Bishop, Kirill Lazebnik, Mariusz Urbański. Mathematische Annalen. volume 387, pages 1777–1818, 2023.
10. Interpolation of Power Mappings. Jack Burkart, Kirill Lazebnik. Revista Matemática Iberoamericana. 39 no. 3, pp. 1181–1200, 2023.
9. Bers Slices in Families of Univalent Maps. Kirill Lazebnik, Nikolai G. Makarov, Sabyasachi Mukherjee. Mathematische Zeitschrift. 300, pages 2771–2808, 2022
8. Quadrature Domains and the Real Quadratic Family. Kirill Lazebnik. Conformal Geometry and Dynamics. 25, 104-125, 2021.
7. Univalent Polynomials and Hubbard Trees. Kirill Lazebnik, Nikolai G. Makarov, Sabyasachi Mukherjee. Transactions of the American Mathematical Society. 374, 4839-4893, 2021.
6. Oscillating Wandering Domains for Functions with Escaping Singular Values. Kirill Lazebnik. Journal of the London Mathematical Society. 103(4): 1643-1665, June 2021.
5. Prescribing the Postsingular Dynamics of Meromorphic Functions. Christopher Bishop, Kirill Lazebnik. Mathematische Annalen , Volume 375, Issue 3-4, December 2019 (1761–1782).
4. Univalent Wandering domains in the Eremenko-Lyubich
Class. Núria Fagella, Xavier Jarque, Kirill Lazebnik. Journal d'Analyse Mathématique. 139(1):369--395, 2019.
3. Several Constructions in the Eremenko-Lyubich class. Kirill Lazebnik. Journal of Mathematical Analysis and Applications, Volume 448, Issue 1, 1 April 2017 (611–632).
2. Zero forcing number, maximum nullity, and path cover number of subdivided graphs. Minerva Catral, Anna Cepek, Leslie Hogben, My Huynh, Kirill Lazebnik, Travis Peters, Michael Young. Electronic Journal of Linear Algebra (23), 2012.
1. On invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions. Bennett, Mike; Lazebnik, Kirill Y; Rault, Patrick X; Singer, Jeffrey A. Journal of Combinatorics and Number Theory (4), 2012.