``Convergence, curvature, and combinatorics in contemporary harmonic analysis''
November 8, 1999
Fourier analysis is an old subject, yet we remain ignorant of the
answers to basic questions, even about convergence of Fourier series,
in dimensions greater than one. Moreover, these issues are directly relevant
to partial differential equations. Many prominent unresolved issues
are related to curvature, and thereby to an absence of arithmetic
structure. In the last few years, combinatorial
arguments have been applied with increasing, though still partial,
success. In this talk I'll try to indicate some of the mathematical
characters, open problems, ideas, and interconnections in this
ongoing drama.