### Harmonic analysis and the geometry of fractals

- Series
- School of Mathematics Colloquium
- Time
- Thursday, February 19, 2015 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Professor Izabella Laba – University of British Columbia

Singular and oscillatory integral estimates, such as maximal theorems and restriction estimates for measures on hypersurfaces, have long been a central topic in harmonic analysis. We discuss the recent work by the speaker and her collaborators on the analogues of such results for singular measures supported on fractal sets. The common thread is the use of ideas from additive combinatorics. In particular, the additive-combinatorial notion of "pseudorandomness" for fractals turns out to be an appropriate substitute for the curvature of manifolds.