Related papers: A geometric view of rational Landen transformation…
The geometric realizations of Lusztig's symmetries of symmetrizable quantum groups are given in this paper. This construction is a generalization of that in [19].
In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.
This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…
In this paper, the primary goal is to offer additional insights into the value iteration through the lens of switching system models in the control community. These models establish a connection between value iteration and switching system…
A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
In this lectures I explain a connection between geometric invariant theory and entanglement, and give a number of examples how this approach works.
We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the "discretization by B\"{a}cklund transformations" point of view. We collect both classical formulas of XIXth century…
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given…
The geometry of an admissible B\"acklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite--dimensional skeleton which is the universal…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
The image and the inverse image of a polyhedron under a linear transformation are polyhedrons.
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of…
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the…
We reconsider some subtle points concerning the relativistic treatment of the gravitational fields generated by spherically symmetric structures.
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.