83 citations · 542 across the 80 of their papers we have counts for
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When different norms lead to same billiard trajectories?
Arseniy Akopyan, Roman Karasev
In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection la…
Stronger counterexamples to the topological Tverberg conjecture
S. Avvakumov, R. Karasev, A. Skopenkov
Denote by the -dimensional simplex. A map is an almost -embedding if whenever are pairw…
Huang's theorem and the exterior algebra
Roman Karasev
In this note we give a version of Hao Huang's proof of the sensitivity conjecture, shedding some light on the origin of the magical matrix in that proof. For the history of the…
Envy-free division using mapping degree
Sergey Avvakumov, Roman Karasev
In this paper we study envy-free division problems. The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and f…
Mahler's conjecture for some hyperplane sections
Roman Karasev
We use symplectic techniques to obtain partial results on Mahler's conjecture about the product of the volume of a convex body and the volume of its polar. We confirm the conjectur…