Past

Basque Center for Applied Mathematics

The convex hull of space curves with totally positive torsion

Decoupling and discrete restriction inequalities have been very fruitful in recent years to solve problems in additive combinatorics and analytic number theory. In this talk I will present some work in decoupling for Cantor sets, including Cantor sets on a parabola, decoupling for product sets, and give applications of these results to additive combinatorics.

Decoupling, Cantor sets, and additive combinatorics

Decoupling and discrete restriction inequalities have been very fruitful in recent years to solve problems in additive combinatorics and analytic number theory. In this talk I will present some work in decoupling for Cantor sets, including Cantor sets on a parabola, decoupling for product sets, and give applications of these results to additive combinatorics.

Decoupling for Cantor sets on the parabola

Decoupling estimates aim to study the “amount of cancellation” that can occur when we add up functions whose Fourier transforms are supported in different regions of space. In this talk I will describe decoupling estimates for a Cantor set supported in the parabola.

Interactions between Geometric measure theory, Singular integrals, and PDE

The sensitivity theorem

he sensitivity theorem (former sensitivity conjecture) relates multiple ways to quantify the complexity, or lack of “smoothness”, of a boolean function f:{0,1}^n -> f : The minimum degree of a polynomial p(x):R^n -> R that extends f, the sensitivity s(f), and the block sensitivity bs(f).

Decoupling, Cantor sets and additive combinatorics

Decoupling and discrete restriction inequalities have been very fruitful in recent years to solve problems in additive combinatorics and analytic number theory. In this talk I will present some work in decoupling for Cantor sets, including Cantor sets on a parabola, decoupling for product sets, and give applications of these results to additive combinatorics.

Summer School on discrete analysis and complexity of quantum algorithms

Brascamp-Lieb inequalities Summer School

Uniform boundedness in operators parametrized by polynomial curves

Multiple results in harmonic analysis involving integrals of functions over curves (such as restriction theorems, convolution estimates, maximal function estimates or decoupling estimates) depend strongly on the non-vanishing of the torsion of the associated curve.