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^...

# Publications

## Pages

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...

We explore the space of consistent three-particle couplings in \mathbb Z_2-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity,...

We present a brief survey of rigorous results on the asymptotic behavior of correlations between two local functions as the distance between their support diverges, concentrating on the Ising...

We give a description of the operad formed by the real locus of the moduli space of stable genus zero curves with marked points \overline{{\mathcal M}_{0,{n+1}}}({\mathbb R}) in terms of a...

We complete the analysis of the extremal eigenvalues of the the adjacency matrix A of the Erdős-Rényi graph G(N,d/N) in the critical regime d \asymp \log N of the transition uncovered in [arXiv:...

We develop the general theory of the angular N-point spectra and derive the cosmic variance on the light cone. While the angular bispectrum and the trispectrum are well developed in literature,...

While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed curves can be very complicated, the span of the 0-dimensional tautological cycles is always...

We apply the large-charge limit to the first known example of a four-dimensional gauge-Yukawa theory featuring an ultraviolet interacting fixed point in all couplings. We determine the energy of...

We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the...

We address the spectral problem of the normal quantum mechanical operator associated to the quantized mirror curve of the toric (almost) del Pezzo Calabi--Yau threefold called local \mathbb{P}^2...