Science Festival: A mathematical evening

17.30-17.40 Introduction

17.40-17.55 Ioanna Motschan-Armen: The mathematical modelling of biological cells

In this talk, I will present two research topics from my PhD on computational mathematics, united by the modelling of biological cells. The first focuses on stochastic partial differential equations on a sphere, modelling time-evolving surfaces like cell membranes. The second explores electropermeabilization (EP), where short electric pulses increase cell membrane permeability. EP is used to deliver drugs into cells, but its mechanisms remain unclear, making numerical simulations essential to understand the underlying processes.

18.55-18.15 Erik Jansson: Microscopy and mathematics

Understanding protein structures using microscopy is crucial for instance for advancing drug discovery. Cryo-electron microscopy (cryo-EM)  is a technique that captures 2D images of frozen biological molecules from different angles using an electron microscope. These images are then used to reconstruct the molecule’s 3D structure, revealing its shape and function. From a mathematician's point of view, this leads to interesting questions. Mainly, the problem of reconstructing the 3D structure from 2D scans is an inverse problem, and these problems are generally ill-posed, meaning in this case that several similar protein conformations result in the same projection. So how can we solve it? In this talk, I hope to convey my perspective on some of these questions.

18.15-18.35 Petar Jovanovski: What can math tell us about cellular oscillations 

Chemical reaction networks describe how substances interact and change over time, often modeling processes like biological cycles or chemical reactions in cells. These systems are complex and challenging to study. We developed a new method to improve simulation accuracy, capturing key behaviors like oscillations. Additionally, we designed an algorithm that integrates real-world data into simulations, making it more effective than similar approaches that do not use data-driven simulations.

18.35-19.00 Pause

19.00-19.20 Johan Ulander: Why computer simulations should preserve key physical features of the modelled phenomena

Computer simulations are needed for understanding and predicting real-world phenomena. To be reliable, simulations must be accurate and should preserve key features of the modelled phenomena. For instance, stock prices cannot be negative and hence simulations of stock prices that are negative are not physically relevant. This talk explores algorithms that are guaranteed to preserve key features of the modelled phenomena.

19.20-19.50 Olle Häggström: Can AI be conscious?

AI development is currently advancing at breakneck speed. Might we be approaching the point where AI becomes conscious? Or might we already have reached it?  We do not currently know the answers to these questions, but we urgently need to figure them out, because getting them wrong – either by erroneously declaring the AIs to be conscious or erroneously dismissing them as non-conscious – could have very bad consequence.

19.50-20.00 Closing