Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Localization errors of the stochastic heat equation

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021