Annual Symposium "Connecting Mathematical Methods across Utrecht University" - Edition 2024

Researchers from different research areas often use similar mathematical techniques and struggle with similar problems. Nevertheless, the various fields involved develop in most cases without being aware of each other’s progress and of the existing state-of-the art tools used by mathematicians. The aim of this annual symposium is therefore to bring together the people at Utrecht University that apply quantitative methods in their research and in that manner stimulate interaction and cross-fertilization. Everyone is welcome!

Participation is free, but registration is kindly requested (see end of this page).

Content

The symposium consists of a number of talks in which mathematical methods are used for biology, linguistics, social sciences, economics, and health, all accessible to a broad audience.

Preliminary Programme

13:00-13:25 Lunch

13:25-13:30 Opening by Prof. dr. Ieke Moerdijk

13:30-14:00 "Dynamical systems in MRI" by Dr. Allessandro Sbrizzi (Computational Imaging group, UMC Utrecht)

14:00-14:15 Discussion & Coffee/Tea

14:15-14:45 "Infectious diseases in ecosystems" by Prof. dr. ir. Hans Heesterbeek (Department Population Health Sciences)

14:45-15:00 Discussion & Coffee/Tea

15:00 -15:30 "Physics ∩ Machine Learning" by Dr. Ro Jefferson (Institute for Theoretical Physics and Department of Information and Computing Sciences)

15:30-15:45 Discussion & Coffee/Tea
 
15:45-16:15 "Unraveling the behavior of the Earth’s magnetic field using Micromagnetic Tomography" by Dr. Lennart de Groot (Department of Earth Sciences)

16:15-16:30 Discussion & Coffee/Tea

16:30-17:00 "Mathematics and social science" by Prof. dr. Daniel Oberski (Department of Methodology and Statistics)

Lectures Overview

Dynamical systems in MRI
Different types of dynamics play a role in Magnetic Resonance Imaging (MRI). The governing spin dynamics equation, formulated by Felix Bloch in 1946, is a linear, time-varying system of ordinary differential equations (ODEs). Beyond spin dynamics, physiological dynamics such as respiration and cardiac activity can also be targeted. While conventional MRI protocols strive to be insensitive to these effects, new directions in the field aim to identify the different dynamics at play, shedding new light on the characteristics of soft tissue. This requires careful design of measurement and reconstruction strategies, which are cast as large-scale non-linear optimization problems.

by Dr. Allessandro Sbrizzi (Computational Imaging group, UMC Utrecht)

Infectious diseases in ecosystems
Each pathogen has a range of host species that it can infect. This range can be small or large, but there are, for each pathogen, many more species that are not susceptible to that pathogen. An ecosystem is a complex system where species interact in many ways, for example, through consumer-resource relations, competition for food and habitat, symbiosis, mutualism et cetera. These interactions moreover occur at and between various trophic levels, such as, roughly speaking, carnivores, herbivores, and plants. These ecological interactions between all species in an ecosystem have impact on the dynamics of the host species for any specific pathogen and the dynamics of that pathogen. Vice versa, the epidemiological interactions in the pathogen-host sub-system influence the dynamics of the non-hosts in the broader ecosystem. To understand the dynamics of pathogens in nature, and the role that pathogens play in making ecosystems stable, resilient, and biodiverse, one must study pathogens in their complex ecosystem context.

by Prof. dr. ir. Hans Heesterbeek (Department Population Health Sciences)

Physics ∩ Machine Learning
Machine learning has become both powerful and ubiquitous, but remains a black box whose internal workings are still largely unclear. In this talk, I will discuss some interesting mathematical connections between theoretical physics and deep neural networks in particular, which collectively motivate a physics-based approach towards a theory of deep learning.

by Dr. Ro Jefferson (Institute for Theoretical Physics (ITP) and Department of Information and Computing Sciences)

Unraveling the behavior of the Earth’s magnetic field using Micromagnetic Tomography
Volcanic rocks preserve the state of the Earth’s magnetic field at the time of their cooling and solidification. As the rocks cool through their Curie temperature, the iron-bearing particles within them become magnetized in alignment with the ambient magnetic field. By collecting samples and measuring their magnetic moments in the lab, it is possible to reconstruct the past direction and intensity of the Earth’s magnetic field. Traditionally, this was done by analyzing bulk rock samples, which provided a statistical average of the magnetic moments from millions of particles at once. However, the recording properties of these iron-oxide-bearing particles vary significantly depending on factors such as size, shape, and chemical composition. Some particles are highly reliable recorders of past magnetic fields, while others are not. Identifying and isolating the magnetic moments of individual particles with optimal recording properties would represent a major advance in improving the accuracy and reliability of paleomagnetic data. To this end we are developing 'Micromagnetic Tomography', an exciting new technique that uses a combination of magnetic microscopy and micro-CT data. Through mathematical inversion, the magnetic moments of individual grains within a sample are determined. Here, I will discuss the current state-of-the-art of Micromagnetic Tomography and explore future developments aimed at further enhancing the precision and quality of its results.

by Dr. Lennart de Groot (Department of Earth Sciences)

Mathematics and social science
Mathematics and social science have a long history together. Mathematical models are popular in a few subfields of social science, and -- although few remember this fact -- many statistical techniques now used throughout science were originally invented by social scientists. But in spite of their long relationship, I feel that, within the social sciences as a whole, mathematics has not been able to reach its full "unreasonable effectiveness" - yet. This is a shame, since many of humans' most pressing problems would benefit from more actionable knowledge on how people and society work. In this talk, I will point out a few issues on which I believe we have grown apart and could come back together, hoping to inspire you to make an impactful contribution to social science.

by Prof. dr. Daniel Oberski (Department of Methodology and Statistics)

To attend the symposium, please signup below before 15:00 on Friday October 25.