Kazhdan's property (T) for $\operatorname{Aut}(F_n)$ and $EL_n(\mathcal{R})$

Kazhdan’s property (T) for groups has a number of applications in pure and applied mathematics. I will report the recent development by several hands on the heavily computer assisted methods of proving property (T) (with math rigor), which eventually confirmed property (T) for $\operatorname{Aut}(F_n)$, $n>3$, thus solving a well-known problem in geometric group theory. I then talk about my recent human effort in coping with the computer assisted proof.

Biography

Narutaka Ozawa is working on theory of operator algebras on Hilbert spaces and on the functional analytic aspects of the group theory, with an emphasis on the interplay between these subjects.

• Ph.D. in Mathematics, Texas A&M University, May 2001.

• Professor, Research Institute for Mathematical Sciences, Kyoto University.

• Sloan Research Fellowships in 2005.

• ICM Invited Speaker (Operator Algebras and Functional Analysis), Madrid, 2006.

• Spring Prize (Mathematical Society of Japan), 2009.

• Awards for Science and Technology (MEXT Japan), 2021.