Past

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.

Harmonic Analysis and Analytic Number Theory, Dual trimester program

Harmonic Analysis and Analytic Number Theory, Dual trimester program

UCLA Math 33B: Differential equations - Spring 2021

First-order, linear differential equations; second-order, linear differential equations with constant coefficients; power series solutions; linear systems. TA for Sections 1C, 1D. (Taught by [Chengxi Wang](http://www.math.ucla.edu/~chwang)). Link to the [CCLE site](https://ccle.ucla.edu/course/view/21S-MATH33B-1?section=15).

Decoupling for Cantor Sets

In this talk we discuss sharp ℓ2L2n estimates for Cantor sets. These estimates are related to the work of Biggs bounding the number of solutions to a certain type of Diophantine equations for integers contained in Ellipsephic sets, sets of numbers missing certain digits in base p.

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.