An information-theoretic approach towards the Kneser-Poulsen conjecture
Gautam Aishwarya (Technion))
| Speaker |
Gautam Aishwarya (Technion))
|
|---|---|
| When |
Mar 02, 2023
from 10:00 AM to 11:00 AM |
| Where | Auditorium, Ground Floor, TIFR CAM |
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Abstract: The Kneser-Poulsen conjecture in discrete geometry asserts that the volume of a union of balls in Euclidean space must decrease if their centres are brought closer. In this talk, we will propose an information-theoretic approach to tackle this problem. Our approach revolves around a broad question regarding whether Rényi entropies of independent sums decrease when one of the summands is contracted by a 1-Lipschitz map. The techniques we use to settle several cases of this question will be illustrated through prototype examples. (Based on joint work with Irfan Alam, Dongbin Li, Sergii Myroshnychenko, and Oscar Zatarain-Vera)