The estimation of three-dimensional fixed effects panel data models

The paper introduces for the most frequently used three-dimensional fixed effects panel data models the appropriate Within estimators. It analyzes the behaviour of these estimators in the case of no-self-flow data, unbalanced data and dynamic autoregressive models.panel data, unbalanced panel, dynamic panel data model, multidimensional panel data, fixed effects, trade models, gravity models, FDI

Unification mechanism for gauge and spacetime symmetries

A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so called Levi factor of the gauge group needs to be compact semisimple, not the entire gauge group. This allows a non-conventional supersymmetry-like extension of the gauge group, glueing together the gauge and spacetime symmetries, but not needing any new exotic gauge particles. It is shown that this new relaxed requirement on the gauge group is nothing but the minimal condition for energy positivity. The mechanism is demonstrated to be mathematically possible and physically plausible on a U(1) based gauge theory setting. The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman-Mandula no-go theorems in a non-supersymmetric way.Comment: 20 pages, 4 figure

Recent developments in quantum mechanics with magnetic fields

We present a review on the recent developments concerning rigorous mathematical results on Schr\"odinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon.Comment: Update of the previous versions; some more references added and typos and some minor errors correcte

Linearization of group stack actions and the Picard group of the moduli of \SL_r/\mu_s-bundles on a curve

We first study the descent theory of line bundles under a morphism which is tors or under a group stack and then use this technical result to determine the exact structure of \Pic(\M_G) where G=\SL_r/\mu_s (we include a minor modification to explain the genus 0 case).Comment: 13 pages, PlainTe

Random matrices, log-gases and Holder regularity

The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution. We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution. We also show related results for log-gases that represent a universal model for strongly correlated systems. Finally, in the spirit of Wigner's original vision, we discuss the extensions of these universality results to more realistic physical systems such as random band matrices.Comment: Proceedings of ICM 201