Dicrete and convex geometry, with essential use of topological methods.
Main publications:
R.N. Karasev, “Transversals for the families of translates of a two-dimensional convex compact set”, Discrete and Computational Geometry, 24:2/3 (2000), 345–353
R.N. Karasev, “Tverberg's transversal conjecture and analogues of nonembeddability theorems for transversals”, Discrete and Computational Geometry, 38:3 (2007), 513–525
R.N. Karasev, “Periodic billiard trajectories in smooth convex bodies”, Geometric and Functional Analysis, 19:2 (2009), 423–428
R.N. Karasev, “The genus and the category of configuration spaces”, Topology and its Applications, 156:14 (2009), 2406–2415
V.L. Dol'nikov, R.N. Karasev, “Dvoretzky type theorems for multivariate polynomials and sections of convex bodies”, Geometric and Functional Analysis, 21:2 (2011), 301–318
R.N. Karasev, F.V. Petrov, “Partitions of nonzero elements of a finite field into pairs”, Israel Journal of Mathematics, 192 (2012), 143–156
R.N. Karasev, “A simpler proof of the Boros–Füredi–Bárány–Pach–Gromov theorem”, Discrete and Computational Geometry, 47:3 (2012), 492–495
R.N. Karasev, “An analogue of Gromov's waist theorem for coloring the cube”, Discrete and Computational Geometry, 2013
