Dicrete and convex geometry, with essential use of topological methods.

1. 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      
2. R.N. Karasev, “Tverberg's transversal conjecture and analogues of nonembeddability theorems for transversals”, Discrete and Computational Geometry, 38:3 (2007), 513–525      
3. R.N. Karasev, “Periodic billiard trajectories in smooth convex bodies”, Geometric and Functional Analysis, 19:2 (2009), 423–428  
4. R.N. Karasev, “The genus and the category of configuration spaces”, Topology and its Applications, 156:14 (2009), 2406–2415  
5. 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  
6. R.N. Karasev, F.V. Petrov, “Partitions of nonzero elements of a finite field into pairs”, Israel Journal of Mathematics, 192 (2012), 143–156  
7. R.N. Karasev, “A simpler proof of the Boros–Füredi–Bárány–Pach–Gromov theorem”, Discrete and Computational Geometry, 47:3 (2012), 492–495  
8. R.N. Karasev, “An analogue of Gromov's waist theorem for coloring the cube”, Discrete and Computational Geometry, 2013  

• P.G. Demidov Yaroslavl State University
• Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
• Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region