MATH Seminar
| Title: Plank Problems: Discrete Geometry and Convexity |
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| Job Talk: Combinatorics |
| Speaker: Alexander Polyanskii, Senior Research Fellow of MIPT |
| Contact: Liana Yepremyan, liana.yepremyan@emory.edu |
| Date: 2023-01-27 at 10:00AM |
| Venue: https://emory.zoom.us/j/7744657281?pwd=TTFuLzYrVVUybkY4UlNmY0NINXNqdz09 |
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| Abstract: 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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