Topics on stochastic optimization and long-time approximation of stochastic processes
Fabien Panloup (Angers)
Stochastic optimization is a way of approximating minima of deterministic functions by a stochastic approach. I will begin my talk by some background on this topic and on the Robbins-Monro algorithm. Then, I will state some recent non-asymptotic results about Ruppert-Polyak algorithm, which is an averaged version of the Robbins-Monro algorithm. In a last part, I will briefly introduce the problem of long-time approximation of diffusion processes and its link with approximation of Gibbs distributions. I will conclude some statistical applications of these methods. This talk is based on collaborations with Sébastien Gadat and Gilles Pagès
Admissibility conjecture for quantum group representations
Biswarup Das (Uniwersytet Wrocławski)
A long-standing open problem in the representation theory of quantum groups is to decide whether the following statement is true or false: Every finite dimensional, unitary representation of (locally) compact quantum group ''factors'' in a suitable sense, through a representation of some matrix quantum group. This conjecture came up first in a work of P. Sołtan, and later on it kept featuring in many subsequent works on representation theory of (locally) compact quantum groups. We will give a partial solution to this conjecture, through proving that for a large class of (locally) compact quantum groups, this is true. Based on a joint work with P. Salmi and M. Daws.
Ujemne zależności i własność "hyperuniformity" dla procesów punktowych
prof. Ryszard Szekli (Uniwersytet Wrocławski)
Podamy dwie równoważne definicje ujemnego stowarzyszenia dla procesów
punktowych. Jako przykłady procesów punktowych ujemnie stowarzyszonych
tzw. "determinantal" oraz procesy "mixed sampled". Przypomnimy związki
procesów "determinantal" z procesami punktowymi Gibbsa i z rozkładem
wartości własnych pewnych macierzy losowych. Przypomnimy własność
"hyperuniformity" dla procesów punktowych ilustrując ją klasycznymi i
The ideal of the strongly porous sets in the real line.
Arturo Martinez Celis
In the literature there are many different notions of porosity and one of them is the notion of strong porosity: Given a completely metrizable space X, a subset A of X is a strongly porous set if there is a positive constant p such that for any open ball B of radius r smaller than 1, there is an open ball B' inside of B of radius rp such that B' evades the set A. In this talk we will study the cardinal invariants of the sigma ideal generated by the strongly porous sets of the real line and the Cantor space, their relation with different notions of porosity and with other notions in set theory. In particular we will show the notion of strong porosity induces a combinatorial property on trees and we will see that these trees have a connection with the Sacks forcing and some cardinal invariants related to Martin's axiom.