In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension n \leq 9.

This result, that was...

# Publications

## Pages

We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation...

In this paper, we analyze a number of architectural features of Deep Neural Networks (DNNs), using the so-called Neural Tangent Kernel (NTK). The NTK describes the training trajectory and...

In this note, we study the action of O(d,d) transformations on the integrable structure of two-dimensional non-linear sigma models via the doubled formalism. We construct the Lax pairs...

Even though we know that physical observations are frame independent, the frame dependence of cosmological perturbations is relatively subtle and has led to confusion in the past. In this paper...

We discuss a modified gravity model which fits cosmological observations at a level statistically indistinguishable from \LambdaCDM and at the same time predicts very large deviations from...

Gravitational-wave (GW) detectors can contribute to the measurement of cosmological parameters and to testing the dark-energy sector of alternatives to \LambdaCDM, by using standard sirens. In...

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form...

We present the theoretical model of the "quantum ammeter", a device that is able to measure the full counting statistics of an electron current at quantum time scales. It consists of an Ohmic...

We bootstrap the S-matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S-matrices is strongly constrained...

We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the...

To every rational complex curve C \subset (\mathbf{C}^\times)^n we associate a rational tropical curve \Gamma \subset \mathbf{R}^n so that the amoeba \mathcal{A}(C) \subset \mathbf{R}^n of C is...