We study the second-order phase transition in the d-dimensional Ising model with long-range interactions decreasing as a power of the distance 1/r^{d+s}. For s below some known value s_{∗...}

# Publications

## Pages

We give a microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schrödinger equation (NLS) from many-body quantum theory. The starting point of our proof is...

We describe level-line decompositions of the two-dimensional Gaussian Free Field (GFF) with free boundary conditions. In particular, we point out a simple way to couple the GFF with free...

The d-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power 1/r^{d+s}, admits a second order phase transition with continuously varying...

We survey here the construction and the basic properties of descendent invariants in the theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the rationality of...

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g. in the Chern-Simons field theory and in the theory of...

We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannian. It is a version of the construction...

We discuss, in the context of energy flow in high-dimensional systems and Kolmogorov-Arnol'd-Moser (KAM) theory, the behavior of a chain of rotators (rotors) which is purely Hamiltonian, apart...

We study the fundamental relationship between stable quotient invariants and the B-model for local CP2 in all genera. Our main result is a direct geometric proof of the holomorphic anomaly...

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented....

In this paper, we study positivity phenomena for the e-coefficients of Stanley's chromatic function of a graph. We introduce a new combinatorial object: the {\em correct} sequences of unit...

The relation between the bosonic higher spin {\cal W}_\infty[\lambda] algebra, the affine Yangian of \mathfrak{gl}_{1}, and the SHc algebra is established in detail. For generic \lambda we find...