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Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
elliptic curves the associative Yang-Baxter equation
2010/11/23
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Symplectic reflection algebras and affine Lie algebras
Symplectic reflection algebras affine Lie algebras
2010/11/23
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products c...
There exists no distance-regular graph with intersection array {56,36,9;1,3,48}
distance-regular graph intersection array
2010/11/23
We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distanc...
Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
Fock Spaces Landau Operators time-harmonic Maxwell equations
2010/11/24
We investigate the solution representation for Maxwell equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. This gives a characterization f...
From the Ginzburg-Landau model to vortex lattice problems
the Ginzburg-Landau model vortex lattice problems
2010/11/24
We study minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields. In this regime, minimizing configurations exhibit densely p...
Matrix factorizations and singularity categories for stacks
Matrix factorizations singularity categories for stacks
2010/11/23
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with...
(k+1)-sums versus k-sums
(k+1)-sums k-sums
2010/11/23
Given $k\in \mathbb{N}$ and a subset $A=\{a_{1},...,a_{n}\}$ of $n$ integers, we define $S_{k}=S_{k}(A)=\{\sum_{I}a_{i}:I\in [n]^{(k)}\}$, i.e. $S_{k}$ is the set of integers that may be expressed as...
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on...
An Invariant Theory of Spacelike Surfaces in the Four-dimensional Minkowski Space
Invariant Theory Spacelike Surfaces
2010/11/23
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under con...
Homology computations for complex braid groups
Homology computations complex braid groups
2010/11/23
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these gro...
Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context
Central limit theorem the robust log-regression wavelet estimation
2010/11/23
In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is chara...
On the mean Euler characteristic of contact manifolds
the mean Euler characteristic contact manifolds
2010/11/23
We express the mean Euler characteristic of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact ...
Integrable representations of involutive algebras and Ore localization
Integrable representations involutive algebras Ore localization
2011/2/24
LetAbe a unital algebra equippedwith an involution (·)†, and suppose that the multiplicative set S ⊆ A generated by the elements of the form 1 + a†a satisfies the Ore condition.
Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition
Inviscid Large deviation principle the 2D Navier Stokes equations
2010/11/23
Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root ...
Classifying spaces of degenerating mixed Hodge structures, II: Spaces of SL(2)-orbits
Classifying spaces degenerating mixed Hodge structures
2010/11/23
We construct an enlargement of the classifying space of mixed Hodge structures with polarized graded quotients, by adding mixed Hodge theoretic version of SL(2)-orbits. This space has a real analytic ...