The colloquium of the Centre for Mathematical Sciences, Lund University, normally runs once a month, Wednesdays from 14.00 until 15.00 in the Hörmander, Riesz or Gårding lecture halls. It is aimed at the entire Centre for Mathematical Sciences with overview talks by renowned experts about exciting mathematical topics. The purpose of our colloquium is twofold: firstly, it is to provide an inspiring overview of a specific field of mathematics, secondly, it is to bring together students and staff from the entire department and to serve as the proverbial waterhole where contacts are made and maintained. For more information, see the guidelines for colloquium speakers.

The colloquium is organized by Dragi Anevski, Magnus Aspenberg, Magnus Oskarsson, Andreas Langer and Anitha Thillaisundaram. Feel free to contact any one of us for questions or suggestions for colloquia speakers. See also the information for suggesting colloquium speakers.

September 2 at MA:3

Speaker

Liviana Palmisano (KTH)

Title

How stable is chaos? From Smale to the Hénon attractor

Abstract

One of the main questions in dynamical systems is to understand the long-term behavior of a system and how this behavior changes when the system is slightly perturbed. Often, the long-term dynamics is organized around an attractor, a set towards which nearby orbits evolve. Some attractors can have very complicated, chaotic dynamics, while still possessing a strong form of stability known as hyperbolicity.

I will give an overview of the history that led Smale to conjecture that hyperbolicity should describe the typical behavior of dynamical systems. While this picture works well in many one-dimensional settings, it is known to fail in dimension two. I will discuss what can happen beyond the hyperbolic setting, focusing on chaotic attractors and, in particular, on the Hénon attractor. I will discuss as well the case of physical systems coming from biological observations. 

This brings us back to the question of stability: if hyperbolicity is no longer present, what, if anything, survives under small perturbations? I will discuss some results in this direction and ask to what extent Smale's original picture can still survive in a weaker form.

October 7 at MA:3

Speaker

Fadoua Balabdaoui (ETH Zürich)

Title

Unmatched linear regression: Asymptotic results under identifiability

Abstract

Consider the regression problem where the response and the covariate  are unmatched. Under this scenario we do not have access to pairs of observations from their joint distribution, but instead we have separate data sets of responses and covariates, possibly collected from different sources. We study this problem assuming that the regression function is linear and the noise distribution is known or can be estimated. We introduce an estimator of the regression vector based on deconvolution (the DLSE) and demonstrate its consistency and asymptotic normality under  parametric identifiability.  Under non-identifiability of the regression vector but identifiability of the distribution of the predictor, we construct an estimator of the latter based on the DLSE and show that it converges to the true distribution of the predictor at the parametric rate in the Wasserstein distance of order 1. We illustrate the theory with several simulation results. 

This talk is based on my joint work with Mona Azadkia, Antonio di Noia and Cecile Durot.

October 21 at MH:Gårding

Speaker

Xue-Cheng Tai (NORCE (Norwegian Research Center))

Title

Mathematical explanations of neural networks and transformers

Abstract

TBA

December 9 at MH:Hörmander

Speaker

Eusebio Gardella (Chalmers and the University of Gothenburg)

Title

Operator algebras beyond Hilbert spaces

Abstract

TBA