A Lagrangian subspace L of a weak symplectic vector space is called \emph{split Lagrangian} if it has an isotropic (hence Lagrangian) complement. When the symplectic structure is strong, it is...

# Publications

## Pages

This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras, their main...

In the Euclidean plane, two intersecting circles or two circles which are tangent to each other clearly do not carry a finite Steiner chain. However, in this paper we will show that such exotic...

We review our construction of the Teichmüller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief...

We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE...

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...

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...