Finite Gel'fand pairs and their applications to Probability and Statistics

We present a general introduction to finite Gel’fand pairs and their associated spherical functions yielding different characterizations, examine a few explicit examples, and, for each of these examples, analyze the corresponding probabilistic problem, which will then be solved by applying the general results and the machinery developed for a particular Gel’fand pair

Representation theory of wreath products of finite groups.

This is an exposition on the representation theory of wreath products of finite groups, with many examples worked out

Induced representations and Mackey theory

This is an exposition on Mackey theory for induced representations of finite group

Metacercarias de Digenea en Hyphessobrycon Wajat Almirón & Casciotta, 1999 en la laguna del Parque General Manuel Belgrano, Santa Fe

Los ambientes acuáticos urbanos brindan servicios ecosistémicos valiosos tales como esparcimiento, provisión de agua y control de inundaciones. Sin embargo, muchos de estos servicios entran en riesgo debido a la falta de monitoreo y medidas de manejo que garanticen el mantenimiento de su integridad biológica. El Parque General Manuel Belgrano (PGMB) se encuentra ubicado en la zona sur de la ciudad de Santa Fe y posee una laguna aislada del riacho Santa Fe por un terraplén artificial. Este cuerpo de agua contiene una comunidad de unas 20 especies de peces, con una alta abundancia del pequeño carácido Hyphessobrycon wajat. Este trabajo tuvo como objetivo estudiar los ectoparásitos asociados a la población de H. wajat residente en la laguna del PGMB.Asociación Parasitológica Argentin

Giant Graviton Oscillators

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.Comment: 72 page

Harmonic analysis of the space of S(a)×S(b)×S(c)-invariant vectors in the irreducible representations of the symmetric group.

We compute a basis for the S(a)×S(b)×S(c)-invariant vectors in the irreducible representations of the symmetric group

Examples of Markov chains on spaces with multiplicities

We show how to compute the spectra of several random walks that are invariant for the action of a group G in the case that the action is either not transitive or not multiplicity-free. This extends the classical analysis of stochastic processes developed by Diaconis et. al. in a Gelfand pair setting. In this expository note, we do not present the general theory, but we show the main ideas through examples, avoiding the technical results