Harmonic analysis and the geometry of fractals

School of Mathematics Colloquium
Thursday, February 19, 2015 - 11:00
1 hour (actually 50 minutes)
Skiles 005
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.