The colloquium is organized by Michael Björklund, Dennis Eriksson and Moritz Schauer. Feel free to contact any one of us for questions or suggestions for colloquia speakers. Even if the colloquium for the term is fully booked, suggestions for the Mathematical Sciences Seminar are always welcome.

##### Colloquia 2022

**24/1 (Zoom, https://chalmers.zoom.us/j/66721233488 Password: 699807)Jan Gerken (Chalmers and University of Gothenburg)**

*Geometric deep learning: On the interplay between mathematics and deep neural networks*

The field of geometric deep learning has gained a lot of momentum in recent years and attracted people with different backgrounds such as deep learning, theoretical physics and mathematics. This is also reflected by the considerable research activity in this direction at our department. In this talk, I will give an introduction into neural networks and deep learning and mention the different branches of mathematics relevant to their study. Then, I will focus more specifically on the subject of geometric deep learning where symmetries in the underlying data are used to guide the construction of network architectures. This opens the door for mathematical tools such as representation theory and differential geometry to be used in deep learning, leading to interesting new results. I will also comment on how the cross-fertilization between machine learning and mathematics has recently benefited (pure) mathematics.

**11/10 in Pascal, 15.30-17.00 (Colloquium coffee 15.00-15.28 in the common room)****Jakob Björnberg (University of Gothenburg/Chalmers)***Mathematical works of Hugo Duminil-Copin*

Abstract: Hugo Duminil-Copin is one of the four Fields-medal winners of 2022. He received the prize "for solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four." In this talk I will give an introduction to a selection of his works in this area, and place them within a larger context.

##### Colloquia 2020

**20/1 in PascalTobias Ekholm (Uppsala University)**

*Skeins on Branes*

The HOMFLY polynomial is an invariant of knots in the 3-sphere allowing one to distinguish different knots. It is a two variable polynomial which is defined combinatorially, via so called skein-relations. We give a geometric interpretation of the coefficients of the polynomial as a count of certain holomorphic curves associated to the knot. One of the variables in the HOMFLY accounts for the area or homological degree of the curves, the other for their Euler characteristic. This is in line with predictions by Ooguri and Vafa based on topological string theory. The proof embodies a new method to define invariant counts of holomorphic curves with Lagrangian boundary. This is a mathematically rigorous incarnation of the fact that boundaries of open topological strings create line defects in Chern-Simons theory as described by Witten.

**17/2 in PascalOlle Häggström (Chalmers/GU)**

*AI Alignment, Embedded Agency and Decision Theory*

The term artificial intelligence (AI) had not yet been coined in the days of Alan Turing. Nevertheless, he did foresee the field, and famously predicted that machines would eventually become so capable as to surpass human general intelligence, in which case he suggested that "we should have to expect the machines to take control". The (small but growing) research area known as AI Alignment takes this ominous prediction as a starting point, and aims to work out how to instil the AI with goals that lead to a good outcome (for humans) despite their taking control. Attempts to solve AI Alignment lead to many intriguing philosophical and mathematical questions involving, e.g., the notion of embedded agency, and the fundamentals of decision theory.

**9/3 in PascalLaura Mancinska (University of Copenhagen)**

*Harnessing Quantum Entanglement*

Entanglement is one of the key features of quantum mechanics. It lies at the heart of most cryptographic applications of quantum technologies and is necessary for computational speed-ups. However, given a specific information processing task, it is challenging to find the best way to harness entanglement and we are yet to uncover the full range of its potential applications.

We will see that the so-called nonlocal games provide a rigorous mathematical framework for studying entanglement and the advantage that it can offer. On the one hand, we will take a closer look at specific applications of entanglement, including protocols for certifying proper functioning of untrusted quantum devices. While on the other hand, we will attempt to gain a better understanding of the mathematical structure of entanglement by considering a restricted class nonlocal games. This class will give rise to a natural quantum relaxation for the notion of graph isomorphism.

**20/4 in PascalTom Britton (Stockholm University)**

*Mathematical modelling of infectious disease outbreaks like covid-19 (video from the seminar at Chalmers Play)*

Abstract: Mathematical models for the spread of infectious diseases are used to: better understand spreading mechanisms, determine if a big outbreak is likely to occur and how big it will be, determine if a disease will become endemic, and investigate how various preventive measures can reduce spreading hopefully preventing a major pandemic outbreak or make an endemic disease vanish. Making inference is harder than usual in that the basic events, transmissions, are rarely observed but instead proxies like onset of symptoms are recorded, and also by the fact that these events are dependent rather than independent (as is usually the case).

In the talk I will give an overview of the area with particular focus on emerging outbreaks, including illustrations from the current coronavirus outbreak.

**25/5 in PascalStephen Pankavich (Colorado School of Mines)**

*CANCELLED: The Initial Value Problem of Plasma Dynamics*

**8/6 in PascalMats Andersson (Chalmers/GU)**

*POSTPONED: Computing Geometric Intersections by Complex Analysis*