Évènements

Possible reunion d’equipe

We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erdős-Rényi random graph $G(n,p)$. Recently Acan and Kahn showed that the largest such family contains only $O(n^2/(\log{n})^3)$ cliques, with high probability, which disproved a conjecture of Alon and Spencer. We prove the corresponding lower bound, $\Omega(n^2/(\log{n})^3)$, by considering a random graph process which sequentially selects and deletes near-maximal cliques. The main tool in our analysis is the so-called Differential Equation Method. This is a joint work with Simon Griffiths.

An Introduction to the Boschloo’s Test

The Boschloo’s test is an exact test for comparing two binomial proportions and is closely related to Fisher’s exact test. By avoiding the conservatism inherent in conditioning on fixed margins, it can offer improved performance in small-sample settings. The test is constructed by using Fisher’s p-value as a test statistic and evaluating it under an unconditional framework. The talk will give a brief overview of the idea behind the test and its relationship to classical exact methods.

A Harish-Chandra module is the algebraic « skeleton » of an irreducible continuous representation of a real reductive group. For a given Harish-Chandra module there are typically many continuous representations that correspond to it. In this talk we will explore to what extend continuous representations (in particular on Banach spaces) with the same Harish-Chandra module may differ from each other, and discuss some relations to automorphic forms. (This is joint work with Joseph Bernstein, Pritam Ganguly, Bernhard Krötz and Eitan Sayag.)

La variété de Rankin-Selberg est la variété homogène sphérique X=(GL_n x GL_{n+1}) / GL_n, définie sur un corps K. Dans cet exposé, on s’intéressera à différentes notions de spectres associées à X. Pour K un corps local de caractéristique zéro, il s’agira de déterminer l’ensemble des sous-représentations irréductibles de l’espace des fonctions lisses sur X. Je donnerai alors la réponse pour celles qui sont unitaires, complétant des travaux de K.Y. Chan, C. Chen et R. Chen. Pour K un corps global, j’expliquerai comment le spectre de X s’interprète en termes d’une décomposition spectrale automorphe de séries thêta, dont je donnerai ensuite une description explicite. Dans les deux cas, la méthode repose sur l’observation que les résidus des intégrales Zeta de Rankin-Selberg produisent des périodes sur le spectre non-générique.