Related papers: Z_2-systolic-freedom
We show that some simple well studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poschl-Teller…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher-derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is square-free.
In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurence of spin and charge separation.…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
In this article, we use a mechanism introduced by Herman, Marco and Sauzin to show that if a perturbation of a quasi-convex integrable Hamiltonian system is not too small with respect to the number of degrees of freedom, then the classical…
After reformulating Gromov's non-squeezing theorem as an area-inequality, we discuss a seemingly natural higher dimensional generalization.
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this result are: (i) sharp local systolic inequalities for…
Coboundary expansion (with $\mathbb{F}_2$ coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random complexes, property testing, and above all Gromov's topological…
We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We show that there is an unexpected relation between free divisors and stability and coincidence thresholds for projective hypersurfaces.
In this paper we study the Lagrangian Floer theory over $\Z$ or $\Z_2$. Under an appropriate assumption on ambient symplectic manifold, we show that the whole story of Lagrangian Floer theory in \cite{fooo-book} can be developed over $\Z_2$…
We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros…
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors. This is followed by a description of an asymptotic version of the Kerr theorem that produces regular asymptotically shear free null geodesic…
A new parafermionic algebra associated with the homogeneous space $A^{(2)}_2/U(1)$ and its corresponding $Z$-algebra have been recently proposed. In this paper, we give a free boson representation of the $A^{(2)}_2$ parafermion algebra in…
A glossary overview of the phenomenological studies of quasi-realistic free fermionic heterotic string models is presented. I elaborate on the correspondence of these models with Z2XZ2 orbifolds.
In the present work we investigate a new statistical ensemble, which seems logical to be entitled the open one, for the case of a one-component system of ordinary particles. Its peculiarity is in complementing the consideration of a system…
With the advent of quantum simulators, exploring exotic collective phenomena in lattice models with local symmetries and unconventional geometries is at reach of near-term experiments. Motivated by recent progress in this direction, we…