The colloquium of the Center for Mathematical Sciences, Lund University, normally runs once a month, Wednesdays from 14.15 until 15.15 in the Hörmander 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 Goffeng, Magnus Oskarsson, Tony Stillfjord 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.

August 28 at MH:Riesz

Speaker

Frank Giraldo (Naval Postgraduate School)

Title

Element-based Galerkin Methods in Atmospheric Modeling

Abstract

In this talk, I will present the role that element-based Galerkin (EBG) methods have had in atmospheric modeling. I will describe the experiences of my group and collaborators to remedy the identified weaknesses and emphasize the strengths. Among EBG methods, I will describe not only spectral element and discontinuous Galerkin methods, but also flux differencing which invariably must include a discussion on kinetic-energy-preserving and entropy-stable methods. This talk is motivated by my group and collaborators’ research in building operational weather prediction models as well as advancing the field for application in climate and space weather. A list of publications on these topics can be found at: https://frankgiraldo.wixsite.com/mysite/publications.

September 11 at MH:Hörmander

Speaker

Kathleen Kohn (KTH)

Title

Algebra & Geometry in Data Science & AI

Abstract

Analyzing big and structured data and understanding modern AI tools require a vast interdisciplinary mathematical toolbox. An intricate geometry governs most data science applications and optimization tasks. This talk highlights how nonlinear algebra can be used to investigate these geometric structures. The tools we discuss are algebraic geometry at heart but driven by applications and interactions with other mathematical disciplines. The applications we focus on in this talk are machine learning with neural networks, 3D reconstruction in computer vision, and maximum likelihood estimation in statistics.

October 9 at MH:Hörmander

Speaker

Laura Mančinska (University of Copenhagen)

Title

The mathematics of quantum functionality certification

Abstract

In this talk, I will introduce the concept of self-testing, which aims to address the fundamental question of how to certify the proper functioning of black-box quantum devices. Self-testing represents the strongest form of quantum functionality certification, enabling a classical user to infer the quantum state and measurements used to produce the observed measurement statistics. Despite its operational definition, in fact self-testing is closely tied to understanding irreducible representations of groups and algebras along with their stability properties. I will survey key self-testing results and discuss outstanding questions in the field.

November 13 at MH:Riesz

Speaker

Steve Oudot (Inria and École Polytechnique)

Title

Differentiable Topological Data Analysis

Abstract

Topological Data Analysis is concerned with the study of the sublevel-sets of functions defined on data. Such objects can be modeled as persistence modules, i.e., functors from  products of totally ordered sets to the category of vector spaces. One of the key properties of persistence modules is their stability under perturbations of their originating functions: this not only validates their use in data analysis contexts, where they are robust to noise in the data, but it also makes it possible to do differential calculus and optimization with them, thus enabling new  applications for instance in deep learning. In this talk I will give a brief introduction to persistence modules, then I will explain how one can equip their category with what looks like a differential structure, to do differential calculus and optimization. My focus will be primarily on the special case where the poset is totally ordered, which appears in many applications and where persistence modules are simpler to work with because they decompose into elementary summands. If time permits I will also touch upon the general setting, in which the structure of persistence modules is significantly more complex and difficult to work with.

November 27 at MH:Riesz

Speaker

Anders Karlsson (Genève and Uppsala)

Title

A fixed-point theorem for isometries

Abstract

Fixed point theorems, such as those of Brouwer and Banach, are of importance throughout the mathematical sciences. In this talk I will explain a new fixed point theorem for isometries. It states that any isometry of a metric space has a fixed point in a generalized sense, which means that the fixed point may not belong to the space itself only to a natural and canonical compactification of it. This is new even for isometries of Banach spaces, and in this case it for example leads to a new proof of the mean ergodic theorem of von Neumann-Carleman with the feature of remaining valid in any Banach space (contrary to the classical statement of F. Riesz). The notion of metric functionals is central and serves as the metric space analog of linear functionals. Other consequences of the fixed point theorem will be mentioned.