Mirror symmetry is a deep conjectural relationship between
complex and symplectic geometry. It was first noticed by string
theorists. Mathematicians became interested in it when string
theorists used it to predict counts of curves on the quintic...
With the notion of interaction with oracles as a unifying theme
of much of my dissertation work, I discuss novel models and results
for property testing and computational learning, with the use of
Fourier analytic and probabilistic methods.
One...
I will describe some recent results and problems regarding
influence of sets of variables on Boolean functions: In 1989 Benny
Chor conjectured that a balanced Boolean function with n variables
has a subset S of size 0.4n with influence (1-c^n) where...
We will discuss recent work on wave evolutions for large data.
Particular emphasis will be placed on concentration compactness
ideas. Amongst others, we will describe a result for wave equations
from R^3 minus the unit ball into the sphere S^3 where...
Application of Plancherel's theorem to integral kernels
approximating compact period functionals yields estimates on
(global) automorphic Levi-Sobolev norms of the functionals. The
utility of this viewpoint can be illustrated in reconsideration
of...
