Shortest movie: Bose-Einstein correlation functions in e+e- annihilations

Bose-Einstein correlations of identical charged-pion pairs produced in hadronic Z decays are analyzed in terms of various parametrizations. A good description is achieved using Levy stable distributions. The source function is reconstructed with the help of the tau-model.Comment: 6 pages, 3 figures, presented at the 5th Budapest Winter School on Heavy Ion Physic

New boundary monodromy matrices for classical sigma models

The 2d principal models without boundaries have $G\times G$ symmetry. The already known integrable boundaries have either $H\times H$ or $G_{D}$ symmetries, where $H$ is such a subgroup of $G$ for which $G/H$ is a symmetric space while $G_{D}$ is the diagonal subgroup of $G\times G$. These boundary conditions have a common feature: they do not contain free parameters. We have found new integrable boundary conditions for which the remaining symmetry groups are either $G\times H$ or $H\times G$ and they contain one free parameter. The related boundary monodromy matrices are also described.Comment: 36 pages, the Poisson structure is develope

Nonstandard Bethe Ansatz equations for open O(N) spin chains

The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is O(2M+1)$\times$O(2N-2M-1). In this case the boundary breaks the "rank" of the O(2N) symmetry leading to nonstandard Bethe Ansatz equations in which the number of Bethe roots is less than as it was in the periodic case. Therefore these cases are similar to soliton-nonpreserving reflections.Comment: 31 pages, 4 figures, numerical checks added to Appendix F, accepted for publication in Nuclear Physics

Vanishing of intersection numbers on the moduli space of Higgs bundles

In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface. We prove that all intersection numbers in the compactly supported cohomology vanish, i.e. "there are no topological L^2 harmonic forms on Hitchin's space". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles of fixed determinant of odd degree over the given Riemann surface. Our proof shows that the vanishing of all intersection numbers in the compactly supported cohomology of Hitchin's space is given by relations analogous to Mumford's relations in the cohomology ring of the moduli space of stable bundles.Comment: 30 pages (published version

Inequalities for Lorentz polynomials

We prove a few interesting inequalities for Lorentz polynomials including Nikolskii-type inequalities. A highlight of the paper is a sharp Markov-type inequality for polynomials of degree at most n with real coefficients and with derivative not vanishing in the open unit disk. The result may be compared with Erdos's classical Markov-type inequality (1940) for polynomials of degree at most n having only real zeros outside the interval (-1,1)

Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve

This is a survey of results and conjectures on mirror symmetry phenomena in the non-Abelian Hodge theory of a curve. We start with the conjecture of Hausel-Thaddeus which claims that certain Hodge numbers of moduli spaces of flat SL(n,C) and PGL(n,C)-connections on a smooth projective algebraic curve agree. We then change our point of view in the non-Abelian Hodge theory of the curve, and concentrate on the SL(n,C) and PGL(n,C) character varieties of the curve. Here we discuss a recent conjecture of Hausel-Rodriguez-Villegas which claims, analogously to the above conjecture, that certain Hodge numbers of these character varieties also agree. We explain that for Hodge numbers of character varieties one can use arithmetic methods, and thus we end up explicitly calculating, in terms of Verlinde-type formulas, the number of representations of the fundamental group into the finite groups SL(n,F_q) and PGL(n,F_q), by using the character tables of these finite groups of Lie type. Finally we explain a conjecture which enhances the previous result, and gives a simple formula for the mixed Hodge polynomials, and in particular for the Poincare polynomials of these character varieties, and detail the relationship to results of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan. One consequence of this conjecture is a curious Poincare duality type of symmetry, which leads to a conjecture, similar to Faber's conjecture on the moduli space of curves, about a strong Hard Lefschetz theorem for the character variety, which can be considered as a generalization of both the Alvis-Curtis duality in the representation theory of finite groups of Lie type and a recent result of the author on the quaternionic geometry of matroids.Comment: 22 pages, minor clarification