Three Miracles in Analysis - Stefan Steinerberger

Описание

Stony Brook Mathematics Colloquium
December 7, 2016
Stefan Steinerberger, Yale University
Three Miracles in Analysis


I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). This part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman.


Slides: http://www.math.stonybrook.edu/Videos/Colloquium/PDFs/20161207-Steinerberger.pdf