Related papers: Variance of the spectral numbers

The link between Frobenius manifolds and singularity theory is well known, with the simplest examples coming from the simple hypersurface singularities. Associated with any such manifold is a function known as the $G$-function. This plays a…

We formulate some conjectures that relates semisimple Frobenius manifolds, their spectral curves and integrable hierarchies.

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function".…

In a recent paper [8], it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus…

We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative) automorphisms. After computing these "eigenspectra" in the…

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in…

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive…

We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum of harmonics almost surely.

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…

The main results of this article are asymptotic formulas for the variance of the number of zeros of a Gaussian random polynomial of degree $N$ in an open set $U \subset C$ as the degree $N \to \infty$, and more generally for the zeros of…

We establish monotonicity formulas for a parabolic frequency function associated with sign-changing solutions to a class of doubly nonlinear parabolic equations of the form $\partial_t u = \mathcal{L}_{p,\varphi} u^q$ on weighted complete…

The semisimple Frobenius manifolds related to the Hurwitz spaces $H_{g,N}(k_1, ..., k_l)$ are considered. We show that the corresponding isomonodromic tau-function $\tau_I$ coincides with $(-1/2)$-power of the Bergmann tau-function which…

Spectrum is an important numerical invariant of an isolated hypersurface singularity, connecting its topological and analytic structures. The well-known Hertling conjecture tells the relation of range and variance of exponents i.e. elements…

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…

For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus $\leq 1$ Virasoro conjecture of…

We review recent developments in the spectral theory of continuum one-dimensional quasicystals, yielding purely singular continuous spectrum for these Schr\"odinger operators. Allowing measures as potentials we can generalize some results…

We define a measure of spectral asymmetry for G_2 and Spin(7) manifolds. We show that this invariant can be computed in terms of characteristic classes and the covariant constant form defining the G_2 or Spin(7) structure.

This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of a quasihomogeneous singularity. One of them is a new conjecture on the characteristic polynomial. It is an…

Using the theory of spherical varieties and especially Frobenius splitting results for symmetric varieties, we give a type independent very short proof of Wahl's conjecture for cominuscule homogeneous spaces for all primes different from 2.

We consider a smooth submanifold $N$ with a smooth boundary in an ambient closed manifold $M$ and assign a spectral invariant $c(\alpha,H)$ to every singular homological class $\alpha\in H_*(N)$ and a Hamiltonian $H$ defined on the…