The Diamant symposium of Fall 2025 will take place on Thursday 20 and Friday 21 November in De Werelt (Lunteren).
Confirmed invited speakers are Ann Dooms (Vrije Universiteit Brussel), Valentijn Karemaker (KdVI UvA), Bhavik Mehta (Imperial College London), Daniel Paulusma (Durham U).
How to contribute a talk
PhD students and postdocs are warmly welcomed to submit a contributed talk (15-20 mins.) to the symposium. In the registration form (see below) there is an option to submit title and abstract. Alternatively, after registration, a title and abstract can be sent at a later date.
Speakers and abstracts
INVISIBLE
Ann Dooms (Vrije Universiteit Brussel)
Can machines think?
Can machines think? This question was posed by Alan Turing in his seminal paper, Computing Machinery and Intelligence, laying the cornerstone for artificial intelligence. Mathematics emerged as the critical tool driving this revolution—but how? In this talk, I will unveil the mathematical foundations powering the technologies that enable machines to “think.” From early theoretical concepts to cutting-edge algorithms, from classification techniques to generative AI. Let us explore how the art of mathematics pushes the limits of machine intelligence.
Valentijn Karemaker (Korteweg-de Vries Institute for Mathematics, UvA)
Moduli spaces – classifying, constructing and counting varieties
Varieties are the main geometric objects whose properties are studied in algebraic and arithmetic geometry. In particular, there are several interesting invariants of varieties we may consider, like dimension, genus etcetera. To study how varieties, and their invariants, change in families, it can be very advantageous to use moduli spaces. You can think of these as parameter spaces, in which each point corresponds to a variety of a certain type – for example, an elliptic curve, with dimension 1 and genus 1. We will discuss several examples of families of varieties, how we can describe them with a moduli space, and how this can help us to classify, construct and count varieties with prescribed invariants.
Bhavik Mehta (Imperial College London)
Formalising polychromatic colourings of integers
A colouring of the integers by finitely many colours can be called polychromatic for a finite set S if every translate of S uses every colour. For a fixed number of colours k, it is known that there is a finite bound g(k) for which every set of size at least g(k) admits a polychromatic k-colouring, and a large computer search was used to help prove g(3) = 4. We discuss the Lean formalisation of both of these results, which mix topology, probability theory, combinatorics, and software verification, and explore how the philosophy of Lean and mathlib enable this process.
Daniel Paulusma (Durham University)
Graph Colouring Under Input Restrictions
For a positive integer k, a k-colouring of a graph G=(V,E) maps every vertex of G to a colour in {1,..,k} such that no two adjacent vertices are coloured alike. The corresponding decision problem is known as Colouring. If k is not part of the input but a fixed integer, then we write k-Colouring instead. It is well known that k-Colouring is NP-complete even if k=3. In this talk we survey some existing results, techniques and open problems for Colouring and k-Colouring for special graph classes. A graph G is H-subgraph-free if G does not contain H as a subgraph, and G is H-free if G does not contain H as an induced subgraph. Moreover, G is probe H-free if G can be made H-free by adding edges to some independent set in G. In particular, we will consider H-free graphs, probe H-free graphs and H-subgraph-free graphs, and we discuss to what extent structural properties of these graph classes can be exploited to obtain efficient algorithms for Colouring and k-Colouring.
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