Grothendieck polynomials were introduced by Lascoux and Schützenberger, and they play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable...

# Publications

## Pages

We study randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree S, vertices are attached one by one, each linked by an edge to a random vertex of...

We consider the S-matrix bootstrap of four dimensional scattering amplitudes with O(3) symmetry and no bound-states. We explore the allowed space of scattering lengths which parametrize the...

We perform a unified systematic analysis of d+1 dimensional, spin \ell representations of the isometry algebra of the maximally symmetric spacetimes AdS_d+1, \mathbb{R}_{1,d} and dS_d+1. This...

The Ratner property, a quantitative form of divergence of nearby trajectories, is a central feature in the study of parabolic homogeneous flows. Discovered by Marina Ratner and used in her...

We show that the loop O(n) model exhibits exponential decay of loop sizes whenever n\geq 1 and x<\tfrac{1}{\sqrt{3}}+\varepsilon(n), for some suitable choice of \varepsilon(n)>0.

It...

Fixed points of scalar field theories with quartic interactions in d=4-\varepsilon dimensions are considered in full generality. For such theories it is known that there exists a scalar function...

The goal of this paper is to investigate the Theta invariant --- an invariant of framed 3-manifolds associated with the lowest order contribution to the Chern-Simons partition function --- in...

Uniform integer-valued Lipschitz functions on a domain of size N of the triangular lattice are shown to have variations of order \sqrt{\log N}.

The level lines of such functions form a...

We prove a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges. This sharpens our previous analysis by including massless scalar...

This text describes the content of the Takagi lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for boolean functions and its...

In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult...