# Colloquium Series Seminar

Metric properties of Banach spaces, Enflo's problem, Pisier's inequality and quantum random variables

A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure.

In the joint paper with Paata Ivanisvili and Ramon Van Handel we prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube, which, in its turn, is based on a certain formula that we used before in improving the constants in scalar Poincare inequality on Hamming cube. I will also show several extensions of Pisier's inequality with ultimate assumptions on a Banach space structure.

Some of our results use approach via quantum random variables.

Zoom Link: https://msu.zoom.us/j/99862364093

Passcode: 391794 Speaker(s): Alexander Volberg (Michigan State University)

In the joint paper with Paata Ivanisvili and Ramon Van Handel we prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube, which, in its turn, is based on a certain formula that we used before in improving the constants in scalar Poincare inequality on Hamming cube. I will also show several extensions of Pisier's inequality with ultimate assumptions on a Banach space structure.

Some of our results use approach via quantum random variables.

Zoom Link: https://msu.zoom.us/j/99862364093

Passcode: 391794 Speaker(s): Alexander Volberg (Michigan State University)

Building: | East Hall |
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Event Type: | Workshop / Seminar |

Tags: | Mathematics |

Source: | Happening @ Michigan from Department of Mathematics |