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Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmanifolds.
On affine motions and bar frameworks in general position
Bar frameworks universal rigidity stress matrices points in general position
2010/12/8
A configuration p in r-dimensional Euclidean space is a finite collection of points (p1, . . . , pn) that affinely span Rr. A bar framework, denoted by G(p), in Rr is a simple graph G on n vertices to...
Edge-intersection graphs of grid paths: the bend-number
Edge-intersection graphs of grid paths bend-number
2010/12/6
We investigate edge-intersection graphs of paths in the plane grid re-garding a parameter called the bend-number. The bend-number is related to the interval-number and the track-number of a graph.
Uniformization of Sierpiński carpets in the plane
Uniformization of Sierpiński carpets plane
2010/12/9
Let Si, i ∈ I, be a countable collection of Jordan curves in the extended complex plane bC that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uni...
A "hybrid plane" with spin-orbit interaction and magnetic field
"hybrid plane" with spin-orbit interaction magnetic field
2010/12/13
We discuss spectral and resonance properties of a Hamiltonian describing motion of an electron moving on a \hybrid surface" consisting on a hal ine attached by its endpoints to a plane under in uence ...
On intersection lattices of hyperplane arrangements generated by generic points
discriminantal arrangements M¨obius function characteristic polyno-mial enumeration of elements
2010/12/8
We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundament...
Lifting, restricting and sifting integral points on affine homogeneous varieties
integral points affine homogeneous varieties
2010/12/13
In [GN2] an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean e...
Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut is at least k, then G contains k edge-disj...
Evolution of plane curves with a curvature adjusted tangential velocity
curvature driven flow of plane curves curvature adjusted tangential velocity
2010/12/6
We study evolution of closed embedded plane curves with the normal veloc-ity depending on the curvature, the orientation and position of a curve. We propose a new method of tangential redistribution o...
Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs
Berenstein-Zelevinsky data affine type $A$
2010/12/10
We give (conjectural) analogs of Berenstein-Zelevinsky data for affine type A. Moreover,by using these affine analogs of Berenstein-Zelevinsky data, we realize the crystal basis of the negative part o...
Representations of Affine and Toroidal Lie Algebras
Representations of Affine Toroidal Lie Algebras
2010/12/1
We discuss the category I of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties.
Some remarks on the planar Kouchnirenko's Theorem
Milnor number delta-invariant Newton non-degenerate
2010/12/13
In this note we consider different notions of non-degeneracy, as introduced by Kouchnirenko, Wall and Beelen-Pellikaan for plane curve sin-gularities. It is known that non-degenerate singularities sat...
Three realizations of quantum affine algebra $U_q(A_2^{(2)})$
Three realizations quantum affine algebra $U_q(A_2^{(2)})$
2010/12/3
We establish explicit isomorphisms between three realizations of the quantum twisted affine algebra Uq(A(2)2 ): the Drinfeld (“current”) realization, the Chevalley realization, and
the so-called RLL ...
On the geometric realization of the inner product and canonical basis for quantum affine $\mathfrak{sl}_n$
Skew Brownian motion advection-diffusion local time
2010/12/14
Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient.
tion of Non Abelian Group Generated by Affine Homotheties on R^n
Homothety orbit density minimal non abelian action
2010/12/14
In this paper, we study the action of non abelian group G generated by affine homotheties on Rn. We prove that G satisfies one of the following properties: (i) there exist a subgroup G of R∗ co...