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
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Sunday, 18 November, 2018
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...
arXiv:1811.07395
Thursday, 15 November, 2018
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...
arXiv:1811.06201
Thursday, 15 November, 2018
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...
arXiv:1811.06853
Monday, 12 November, 2018
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...
arXiv:1811.04812
Monday, 5 November, 2018
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...
arXiv:1811.02055
Wednesday, 31 October, 2018
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...
arXiv:1810.13275
Tuesday, 30 October, 2018
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...
arXiv:1810.12849
Tuesday, 30 October, 2018
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...
arXiv:1810.12923
Saturday, 27 October, 2018
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...
arXiv:1810.11576
Friday, 26 October, 2018
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...
arXiv:1810.11302
Wednesday, 24 October, 2018
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...
arXiv:1810.10541