In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased...

# Publications for year 2018

## Pages

The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results...

While Hartree-Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In...

We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of m^2=n^2+nl+l^2.

Let c_n = c_n(d) denote the number of self-avoiding walks of length n starting at the origin in the Euclidean nearest-neighbour lattice \mathbb{Z}^d. Let \mu = \lim_n c_n^{1/n} denote the...

The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a...

Given a real function f on an interval [a,b] satisfying mild regularity conditions, we determine the number of zeros of f by evaluating a certain integral. The integrand depends on f,f′ and f...

We introduce and study combinatorial equivariant analogues of the Kronheimer--Mrowka homology theory of planar trivalent graphs.

The celebrated Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory describes the universal correlations of eigenvalues on the microscopic scale, i.e....

We prove a local law for the adjacency matrix of the Erd\H{o}s-R\'enyi graph G(N,p) in the supercritical regime pN \geq C\log N where G(N,p) has with high probability no isolated vertices. In...

We study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q>4. Their existence is closely related to the weak first-order phase transition and walking RG...

During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects....