MATH Seminar

Title: Plank Problems: Discrete Geometry and Convexity
Job Talk: Combinatorics
Speaker: Alexander Polyanskii, Senior Research Fellow of MIPT
Contact: Liana Yepremyan,
Date: 2023-01-27 at 10:00AM
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What is the smallest combined width of planks that cover a given convex region in the plane? What happens in higher dimensions? In the 50s, Thoger Bang answered this innocent question of Alfred Tarski and opened a box with many deceptively simple-looking problems. In my talk, I will overview progress in the area and its connection with other fields: theoretical computer science, number theory, and analysis. In particular, I will discuss a joint work with Zilin Jiang confirming Fejes Toth's long-standing zone conjecture and recent results with Alexey Glazyrin and Roman Karasev on a polynomial plank problem, a far-reaching generalization of Bang's theorem.

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