We are pleased to invite you to the 2026 Barbara and Jaroslaw Zemánek Prize in Functional Analysis Award Ceremony, which will take place on 18 November 2026 in Room 321 (3rd floor) at the Institute of Mathematics of the Polish Academy of Sciences, 8 Śniadeckich Street, Warsaw.
This year's laureate, David Jekel (University of Ottawa), will deliver a lecture entitled Contractibility of the unitary group in von Neumann algebras at 14:30.
Laureate's Lecture
David Jekel (University of Ottawa)
Date and time: 18 November 2026, 14:30
Title: Contractibility of the unitary group in von Neumann algebras
Abstract:
A famous result of Kuiper from 1967 showed that the unitary group in B(H), bounded operators on a Hilbert space, is contractible, meaning it can be continuously deformed to a point. Many subsequent works considered analogous problems in von Neumann algebras, certain subalgebras of B(H). The last remaining case was that of II₁ factors, von Neumann algebras that are infinite-dimensional, but behave qualitatively like "finite" objects, where the technique used to prove Kuiper's theorem did not apply. I will show that the unitary group of a separable II₁ factor is contractible with respect to the strong operator topology. The proof uses free convolution to regularize or smooth out the starting unitary, and from there uses functional calculus to move the spectral mass to the point 1.
