Gautam Aishwarya "An information-theoretic approach towards the Kneser-Poulsen conjecture"

Описание к видео Gautam Aishwarya "An information-theoretic approach towards the Kneser-Poulsen conjecture"

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. Some techniques that we have used to settle several cases of this question will be presented along with a selection of open questions we encountered. (Based on joint work with Irfan Alam, Dongbin Li, Sergii Myroshnychenko, and Oscar Zatarain-Vera)

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