Kazhdan’s property (T) and semidefinite programming

Kazhdan’s property (T) and semidefinite programming

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Narutaka Ozawa, Kyoto University

Zoom link:  https://princeton.zoom.us/j/99136657600

Kazhdan's property (T) for groups has a number of applications in pure and applied mathematics. It has long been thought that groups with property (T) are rare among the "naturally-occurring" groups, but it may not be so and it may be possible to observe this by extensive computer calculations. After an introduction, I will present a computer assisted (but mathematically rigorous) method of confirming property (T) based on semidefinite programming with some operator algebraic input. I will report the recent results by several hands that confirmed property (T) of Aut(F_d) for d>3.This solves a well-known problem in geometric group theory.