In these two talks, I will discuss the structure of certain
varieties that depend functorially on the choice of a
finite-dimensional vector space. Examples include the variety of
d-way tensors of "slice rank" at most k and the variety of
degree-d...
The restriction conjecture, one of the most central problems in
harmonic analysis, studies the Fourier transform of functions
defined on curved surfaces; specifically, it claims that the level
sets of such Fourier transforms are relatively small...
In these two talks, I will discuss the structure of certain
varieties that depend functorially on the choice of a
finite-dimensional vector space. Examples include the variety of
d-way tensors of "slice rank" at most k and the variety of
degree-d...
Given a topological dynamical system $(X,T)$ a bounded sequence
$(a_n)$ and $f\in C(X)$ we are interested in the asymptotic
behavior of $$\frac{1}{\sum_{n\leq N}|a_n|}\sum_{n\leq
N}a_nf(T^nx)$$
This will be a survey talk about recent progress on pointwise
convergence problems for multiple ergodic averages along polynomial
orbits and their relations with the Furstenberg-Bergelson-Leibman
conjecture.
