Superradiation from Crystals of High-Spin Molecular Nanomagnets

Phenomenological theory of superradiation from crystals of high-spin molecules is suggested. We show that radiation friction can cause a superradiation pulse and investigate the role of magnetic anisotropy, external magnetic field and dipole-dipole interactions. Depending on the contribution of all these factors at low temperature, several regimes of magnetization of crystal sample are described. Very fast switch of magnetization's direction for some sets of parameters is predicted.Comment: 10 pages, 3 figure

Regina Lectures on Fat Points

These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat points for an audience that was not expected to have much background in commutative algebra or algebraic geometry (although sections 8 and 9 of these notes demand somewhat more background than earlier sections).Comment: 32 pages, 3 figure

Painleve I, Coverings of the Sphere and Belyi Functions

The theory of poles of solutions of Painleve-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.Comment: 33 pages, many figures. Version 2: minor corrections and minor changes in the bibliograph