## Speaker:

Haonan Zhang

## Speaker Link:

## Institution:

UCI

## Time:

Thursday, January 19, 2023 - 11:00am

## Host:

## Location:

RH 306

Bohnenblust--Hille (BH) inequalities are an extension of Littlewood's 4/3 inequality and have found many applications to harmonic analysis. A variant of BH inequalities for Boolean cubes has been proven with constants that are dimension-free and subexponential in degree. Such inequalities have found great applications in learning low-degree Boolean functions. Motivated by learning quantum observables, a quantum analog of BH inequality for Boolean cubes was recently conjectured and resolved unaware of the conjecture. In this talk, we give a simpler proof with better constants. As applications, we study learning problems for quantum observables of low degrees. Joint work with Alexander Volberg.