Masato Mimura (Tohoku U., EPFL Lausanne)

We overview these two notions (the original definition of property (T) has totally different nature to (FH)), and proceed to their strengthening defined by replacing Hilbert spaces with other Banach spaces. They have applications to coarse geometry via "(ordinary or Banach) expander graphs". We discuss theory on these topics, including recent developments.

No serious backgrounds are assumed in this lecture series. Prerequisites are similarities to examples of infinite groups (definitions of SL(n,Z) and SL(n,R), etc.) and to basic functional analysis (definitions of Hilbert spaces, orthogonal complement, unitary representations; Banach spaces, continuous duals, reflexivity, quotient Banach spaces, Lebesgue and sequence L_p spaces, etc.). Some definitions will be recalled during the lectures, if necessary.

Problem list

This will be a two-week course consisting of 6 x 2 hours of lectures and additional problem sessions led by Biswarup Das. The course is aimed at Master and PhD students (It is worth 3 ECTS points).

The lectures will take place on:

Tuesday, 3.10, 14:00-16:00, room 605

Wednesday, 4.10, 14:00-16:00, room 605

Friday, 6.10, 12:00-15:00, room 605

Tuesday, 10.10, 14:00-17:00, room 605

Wednesday, 11.10, 14:00-16:00, room 607

Thursday, 12.10, 12:00-14:00, room 605

Friday, 13.10, 12:00-16:00, room 605

The problem sessions will take place on Tuesdays, 12:00--14:00, room 606. There will be at least six problem sessions during six weeks, starting Tuesday, 3.10.