Heat flow regularisation, Brascamp鈥擫ieb inequality, and convex geometry

  • 22 November 2023
  • 2pm-3pm
  • Sch 1.05
  • Shohei Nakamura

Shohei Nakamura (Birmingham)

This talk is based on the joint work with Hiroshi Tsuji (Osaka, Japan). A close link between Brascamp—Lieb inequality and convex geometry was discovered by Kieth Ball; volume ratio estimate, reverse isoperimetric problem, Buseman-Petty problem etc. In this talk we will report further link to the volume product of a convex body (Blaschke—Santalo inequality and Mahler’s conjecture). Our principal observation is to understand the volume product as a regularising effect of the Ornstein—Uhlenbeck heat flow (hypercontractivity) which is one of  archetype example of Brascamp—Lieb inequality. We then exhibit a wealth of this new link.

 

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