The colloquium is organized by Philip Gerlee, Magnus Goffeng and Richard Lärkäng. 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 Spring 2020

**20/1 in Pascal**

**Tobias 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 Pascal**

**Olle 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 instill 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 Pascal**

**Laura 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 Pascal**

**Tom Britton (Stockholm University)**

*Stochastic Models for Social Networks and Infectious Disease Dynamics*

**25/5 in Pascal**

**Stephen Pankavich (Colorado School of Mines)**

*The Initial Value Problem of Plasma Dynamics*

**8/6 in Pascal**

**Mats Andersson (Chalmers/GU)**

*Computing Geometric Intersections by Complex Analysis*