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
R. N. Karasev, “Протыкание семейства транслятов двумерного выпуклого тела”, Mat. Pros., Ser. 3, 24 (2019), 159–167
2017
2.
R. N. Karasev, “О разбиениях многогранника
на выпуклые части”, Mat. Pros., Ser. 3, 21 (2017), 224–234
2014
3.
Yu. I. Skalko, R. N. Karasev, A. V. Akopyan, I. V. Tsybulin, M. A. Mendel', “Space-marching algorithm for solving radiative transfer problem basedon short-characteristics method”, Computer Research and Modeling, 6:2 (2014), 203–215
2013
4.
R. N. Karasev, “On two conjectures of Makeev”, Zap. Nauchn. Sem. POMI, 415 (2013), 5–14; J. Math. Sci. (N. Y.), 212:5 (2016), 521–526
2012
5.
H. Edelsbrunner, A. Ivanov, R. Karasev, “Current Open Problems in Discrete and Computational Geometry”, Model. Anal. Inform. Sist., 19:5 (2012), 5–17
2011
6.
R. N. Karasev, “Решение задачи про вписывание пятиугольника”, Mat. Pros., Ser. 3, 15 (2011), 206–211
2009
7.
R. N. Karasev, “Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets”, Mat. Sb., 200:10 (2009), 39–58; Sb. Math., 200:10 (2009), 1453–1471
2008
8.
R. N. Karasev, “Topological methods in combinatorial geometry”, Uspekhi Mat. Nauk, 63:6(384) (2008), 39–90; Russian Math. Surveys, 63:6 (2008), 1031–1078
9.
R. N. Karasev, “Dual theorems on central points and their generalizations”, Mat. Sb., 199:10 (2008), 41–62; Sb. Math., 199:10 (2008), 1459–1479
2007
10.
R. N. Karasev, “Genus and the Lyusternik-Schnirelmann category of preimages”, Model. Anal. Inform. Sist., 14:4 (2007), 31–35
2004
11.
R. N. Karasev, “Проективные преобразования, оставляющие на месте окружность”, Mat. Pros., Ser. 3, 8 (2004), 113–122
2000
12.
R. N. Karasev, “Задача об объеме симметризации выпуклого множества”, Mat. Pros., Ser. 3, 4 (2000), 181–187
1998
13.
R. N. Karasev, “On transversals of the family of translates of two-dimensional convex compact”, Zap. Nauchn. Sem. POMI, 252 (1998), 67–77; J. Math. Sci. (New York), 104:4 (2001), 1293–1300
2010
14.
M. V. Balashov, I. I. Bogdanov, R. N. Karasev, “Студенческие математические олимпиады МФТИ”, Mat. Pros., Ser. 3, 14 (2010), 214–224
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