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Publications Influence

Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities

- Alexey Balitskiy
- Mathematics
- 5 December 2015

In this note we apply the billiard technique to deduce some results on Viterbo's conjectured inequality between volume of a convex body and its symplectic capacity. We show that the product of a… Expand

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Another Ham Sandwich in the Plane

- Alexey Balitskiy, A. Garber, R. Karasev
- Mathematics
- 29 July 2013

We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from any k-fan when k is odd and in some cases when k is even. We also give some… Expand

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Equality cases in Viterbo's conjecture related to permutohedra

- Alexey Balitskiy
- Mathematics
- 5 December 2015

In this note we show, using the billiard technique, that the product of a regular permutohedron and a regular simplex delivers an equality in Viterbo's conjecture.

Flip cycles in plabic graphs

- Alexey Balitskiy, Julian Wellman
- Mathematics
- 5 February 2019

Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian $$\text {Gr}^{\ge 0}(n,k)$$… Expand

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Optimality of codes with respect to error probability in Gaussian noise

- Alexey Balitskiy, R. Karasev, Alexander Tsigler
- Mathematics, Computer Science
- ArXiv
- 27 January 2017

TLDR

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On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman

- A. Akopyan, Alexey Balitskiy, M. Grigorev
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 13 May 2016

TLDR

Waist of maps measured via Urysohn width

- Alexey Balitskiy, A. Berdnikov
- Mathematics
- 9 September 2020

We discuss various questions of the following kind: for a continuous map $X \to Y$ from a compact metric space to a simplicial complex, can one guarantee the existence of a fiber large in the sense… Expand

Elementary approach to closed billiard trajectories in asymmetric normed spaces

- A. Akopyan, Alexey Balitskiy, R. Karasev, Anastasia Sharipova
- Mathematics
- 2 January 2014

We apply the technique of K\'aroly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for… Expand

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Geometric Complexity of Planar Drawings

- J. Choi, Alexey Balitskiy
- 2018

We say that a planar drawing of a graph is 1-thick if the distance between the images of any two vertices, a vertex and an edge, and two non-adjacent edges is at least 1. We prove that the cylinder… Expand

Dependence of the heavily covered point on parameters.

- Alexey Balitskiy, R. Karasev
- Mathematics
- 16 February 2016

We examine Gromov's method of selecting a point "heavily covered" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered point on parameters.… Expand