The Ratner property, a quantitative form of divergence of nearby trajectories, is a central feature in the study of parabolic homogeneous flows. Discovered by Marina Ratner and used in her...

# Publications for year 2018

## Pages

We show that the loop O(n) model exhibits exponential decay of loop sizes whenever n\geq 1 and x<\tfrac{1}{\sqrt{3}}+\varepsilon(n), for some suitable choice of \varepsilon(n)>0.

It...

Fixed points of scalar field theories with quartic interactions in d=4-\varepsilon dimensions are considered in full generality. For such theories it is known that there exists a scalar function...

The goal of this paper is to investigate the Theta invariant --- an invariant of framed 3-manifolds associated with the lowest order contribution to the Chern-Simons partition function --- in...

Uniform integer-valued Lipschitz functions on a domain of size N of the triangular lattice are shown to have variations of order \sqrt{\log N}.

The level lines of such functions form a...

We prove a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges. This sharpens our previous analysis by including massless scalar...

This text describes the content of the Takagi lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for boolean functions and its...

In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult...

We give a proof of the replica symmetric formula for the free energy of the Sherrington-Kirkpatrick model in high temperature which is based on the TAP formula. This is achieved by showing that...

We describe new graphical models of the framed little disks operads which exhibit large symmetry dg Lie algebras.

We propose a cosmological scenario involving a single scalar field, \varphi, that is a source of Dark Matter as well as Dark Energy. The Lagrangian density of \varphi contains a second field \...

In this note, we perform the large-charge expansion for non-relativistic systems with a global U(1) symmetry in 3+1 and 2+1 space-time dimensions, motivated by applications to the unitary Fermi...