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

Title: Noncommutative real algebraic geometry of Kazhdan's property (T)

Date/Time: Wednesday, April 30, 2014, 4:30-6:00

Room: 122

Abstract: I will start with a gentle introduction to the emerging (?) subject of "noncommutative real algebraic geometry," a subject which deals with equations and inequalities in noncommutative algebra over the reals, with the help of analytic tools such as representation theory and operator algebras. I will mention some results toward Connes's Embedding Conjecture, and then present a surprisingly simple proof that a finitely generated group has Kazhdan's property (T) if and only if a certain equation in the group algebra is solvable. This suggests the possibility of proving property (T) for a given group by computers. arXiv:1312.5431.