Speaker: **Narutaka Ozawa** (RIMS, Kyoto Univ.)

Title: Kazhdan's property (T) and semidefinite programming

Time/Date: 4:45-6:15pm, Monday, December 25, 2017.

Room: 126

Abstract: 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-arising" groups, but it may not be so and it may be possible to confirm this by extensive computer calculations. After an introduction, I will present a computer assisted (but mathematically rigorously) method of confirming property (T) based on semidefinite programming and some operator algebraic input. I will report the progress recently made in collaboration with M. Kaluba, P. Nowak, and PL-grid, a Polish supercomputer. It confirms property (T) of Aut(F_5), which solves a long-standing problem in geometric group theory, at least partially, leaving the tantalizing question in the case of Aut(F_d), d=4 and d>5, unsettled.