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...

# Publications

## Pages

Given n \geq 2 and 1<p<n, we consider the critical p-Laplacian equation \Delta_p u + u^{p^*-1}=0, which corresponds to critical points of the Sobolev inequality. Exploiting the moving...

The supermeasure whose integral is the genus g vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the corresponding even theta-...

We investigate the weak lensing corrections to the CMB polarization anisotropies. We concentrate on the effect of rotation and show that the rotation of polarisation is a true physical effect...

We consider irrational nilflows on any nilmanifold of step at least 2. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not...

An important non-perturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can...

We present a systematic procedure to extract the perturbative series for the ground state energy density in the Lieb-Liniger and Gaudin-Yang models, starting from the Bethe ansatz solution. This...

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions \Delta of operators in four-dimensional \mathcal{N}=1 superconformal field theories. We show that in...

The background photon temperature \bar T is one of the fundamental cosmological parameters. Despite its significance, \bar T has never been allowed to vary in the data analysis, owing to the...

Given n≥3, consider the critical elliptic equation \Delta u + u^{2^*-1}=0 in \mathbb R^n with u>0. This equation corresponds to the Euler-Lagrange equation induced by the Sobolev embedding H^...

These notes give an introduction to the mathematical framework of the Batalin-Vilkovisky and Batalin-Fradkin-Vilkovisky formalisms. Some of the presented content was given as a mini course by...

We develop a theoretical framework to describe the cosmological observables on the past light cone such as the luminosity distance, weak lensing, galaxy clustering, and the cosmic microwave...