## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, August 14, 2018 — 3:00 PM EDT

**John Sawatzky, Department of Pure Mathematics, University of Waterloo**

"Fourier algebras"

For a given locally compact group *G*, we will discuss the space of matrix coefficients associated with the left regular representation. This space is known as the Fourier Algebra *A*(*G*), and is actually a closed ideal inside the Fourier-Stieltjes algebra *B*(*G*). We will look at a number of interesting properties of *A*(*G*), such as the fact that its spectrum is just *G* itself, that *A*(*G*) has a bounded approximate identity if and only if *G* is amenable, and that if *H* is a closed subgroup of *G* then *A*(*G*)|_{H} = *A*(*G*).

MC 5417

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1