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).
Conference fee & Accommodation
The symposium hotel is De Werelt in Lunteren. There is full DIAMANT support for DIAMANT members, meaning that we cover lunches and coffee breaks on both days, dinner on Thursday, accommodation, and breakfast on Friday. DIAMANT members are those people listed here, as well as their research group members.
Programme
INVISIBLE
Thursday
| 10:00-10:30 | Arrival & coffee |
| 10:30-11:30 | Ann Dooms (Vrije Universiteit Brussel) – Can machines think? |
| 11:30-12:00 | Soumya Sankar (UU) – Solubility of generalized Fermat equations via stacks |
| 12:00-12:30 | Haowen Zhang (UL) – Intersection of Two Quadrics in P^4 Without Quadratic Points Over Global Function Fields |
| 12:30-13:30 | Lunch |
| 13:30-14:00 | Hsin-Yi Yang (UvA) – CM-liftability of abelian varieties |
| 14:00-14:30 | Andrea di Giusto (TU/e) – The asymptotic number of inequivalent codes of a given dimension |
| 14:30-15:00 | Coffee break |
| 15:00-16:00 | Daniel Paulusma (Durham University) – Graph Colouring Under Input Restrictions |
| 16:00-17:00 | Meeting Diamant board + university representatives |
| 17:00-18:30 | Free time |
| 18:30- | Dinner |
Friday
| 8:30-9:00 | Arrival & coffee |
| 9:00-10:00 | Valentijn Karemaker (University of Amsterdam) – Moduli spaces: Classifying, constructing and counting varieties |
| 10:00-10:30 | Gabriëlle Zwaneveld (UvA) – Vu’s conjecture holds for claw-free graphs |
| 10:30-11:00 | Coffee break |
| 11:00-11:30 | Begum Gulsah Cakti (RUG) – Explicit Bounds for the Asymptotic Generalized Fermat Conjecture over Quadratic Fields |
| 11:30-12:00 | Joppe Stokvis (UL) – Quantum algorithms for the hidden shift problem |
| 12:00-13:00 | Lunch |
| 13:00-13:30 | Manoy Trip (Groningen) – Existence of minimal del Pezzo surfaces of degree 1 with conic bundles over finite fields |
| 13:30-14:00 | Hong Jun Ge (TU) – On co-edge-regular graphs with four distinct eigenvalues |
| 14:00-14:30 | Coffee break |
| 14:30-15:30 | Bhavik Mehta (Imperial College London) – Formalising polychromatic colourings of integers |
| 15:30 – | Mastermath discussion |
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.
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.
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.
Soumya Sankar (UU)
Solubility of generalized Fermat equations via stacks
Classical Diophantine problems can often be rephrased in the language of stacks, which allows the use of a wider geometric toolbox for such problems. In this talk I will describe such a rephrasing for a certain family of generalized Fermat equations which correspond to stacky curves of genus less than 1, and use it to discuss solutions to them. This talk is based on joint work with Juanita Duque Rosero, Chris Keyes, Andrew Kobin, Manami Roy and Yidi Wang, and does not assume any prior knowledge about stacks.
Haowen Zhang (UL)
Intersection of Two Quadrics in P^4 Without Quadratic Points Over Global Function Fields
Creutz and Viray recently demonstrated that for the intersection of two quadrics in P^4 —that is, a system of two quadratic forms in five variables—defined over the field of rational numbers, there exist no rational points over any quadratic extension. In this talk, we prove a similar result for global function fields F_p(t) with any odd prime p. Our work provides a negative answer to a question of Colliot-Thélène concerning the existence of quadratic points on such intersections over C_2-fields. This is joint work with Giorgio Navone, Katerina Santicola and Harry Shaw.
Hsin-Yi Yang (UvA)
CM-liftability of abelian varieties
We study when an abelian variety over a finite field, which has sufficiently many complex multiplications (smCM) by a CM field $L/\mathbb{Q}$, lifts to an abelian variety in characteristic zero with complex multiplication (CM) by $L$, i.e., when it admits a CM lifting.
By a result of Chai-Conrad-Oort, an abelian variety over a finite field with smCM by $L$ admits a CM lifting up to $L$-isogeny if it satisfies the so-called residual reflex condition. On the other hand, there is a result by Yu stating that an abelian variety over a finite field with smCM by $L$ admits a CM lifting after base change to the algebraic closure of the finite field if it has so-called good Lie type. In general, it is an open question whether isogenies or field extensions are needed for CM liftability. As an example, we provide a simple supersingular abelian surface over a prime field of characteristic $p>0$, and see that it admits a CM lifting.
Andrea di Giusto (TU/e)
The asymptotic number of inequivalent codes of a given dimension
We investigate the number of equivalence classes of linear codes over a finite field as the blocklength N grows to infinity. We fix the alphabet size q, and we derive explicit asymptotic formulas for the number of equivalence classes of a given dimension K under the three standard notions of equivalence of coding theory. Our approach also yields an exact asymptotic expression for the sum over K of all q-binomial coefficients N-choose-K as N goes to infinity, which is of independent interest and resolves an open question in this context. Finally, we establish a natural connection between these asymptotic quantities and certain discrete Gaussian distributions that were first studied in connection with the Brownian motion, highlighting an interesting connection with probability theory.
Gabriëlle Zwaneveld (UvA)
Vu’s conjecture holds for claw-free graphs
Given a graph $G$, let $\Delta_2(G)$ denote the maximum number of neighbors any two distinct vertices of $G$ have in common.
Vu (2002) proposed that, provided $\Delta_2(G)$ is not too small as a proportion of the maximum degree $\Delta(G)$ of $G$, the chromatic number of $G$ should never be too much larger than $\Delta_2(G)$. We make a first approach towards Vu’s conjecture from a structural graph theoretic point of view.
We prove that, in the case where $G$ is claw-free, indeed the chromatic number of $G$ is at most $\Delta_2(G)+3$. This is tight, as our bound is met with equality for the line graph of the Petersen graph. Moreover, we can prove this in terms of the more specific parameter that bounds the maximum number of neighbors any two endpoints of some edge of $G$ have in common. Our result may also be viewed as a generalization of the classic bound of Vizing (1964) for edge-coloring.
Based on joint work with Linda Cook, Ross Kang and Eileen Robinson.
Begum Gulsah Cakti (RUG)
Explicit Bounds for the Asymptotic Generalized Fermat Conjecture over Quadratic Fields
The asymptotic generalized Fermat conjecture (AGFC) predicts that for a number field $K$, and non-zero elements $A$, $B$, $C$ of $\mathcal{O}_K$ such that $A\omega_1+B\omega_2+C\omega_3\neq0$ for any root of unity $\omega_1,\omega_2,\omega_3$ in $K$, there is a constant $\mathcal{B}(K,A,B,C)$ such that for all primes $p>\mathcal{B}(K,A,B,C)$, the equation $Ax^p+By^p+Cz^p=0$ has only trivial solutions in $K$. Even though there has been promising progress in proving AGFC over general number fields, it remains unclear whether the bound $\mathcal{B}(K,A,B,C)$ is effectively computable. In this talk, using the modular approach, we will study the equation $d^rx^p+y^p+z^p=0$ over small quadratic fields $\mathbb{Q}(\sqrt{d})$ of class number one. While discussing the differences between working over real quadratic or imaginary quadratic fields, we will show that the AGFC holds for this case. Moreover, we will explore how the bounds $B(K)$ in our results are effectively and explicitly computable.
Joppe Stokvis (UL)
Quantum algorithms for the hidden shift problem
Quantum computers allow for a computational speedup of certain algebraic problems, for example Shor’s algorithm for integer factorisation. In this talk I will give an introduction to quantum algorithms and discus an algorithm for the hidden shift problem. Given two complex functions $f$ and $g$ on an abelian group such that $f(x+s) = g(x)$ for all $x$ in the group, the problem is to determine the hidden shift $s$. The presented algorithm is especially useful for a class of functions called bent functions.
Manoy Trip (RUG)
Existence of minimal del Pezzo surfaces of degree 1 with conic bundles over finite fields
Every rational surface is birational to a conic bundle or a del Pezzo surface. In this talk, we consider surfaces over finite fields that are both del Pezzo surfaces and conic bundles. We focus on surfaces which are minimal and have degree (defined as the self-intersection number of the canonical divisor) equal to 1. We give a classification based on the configuration of the singular fibers of the conic bundle structure, and discuss an answer to the following question: for which values of q can each of these configurations exist on a del Pezzo surface with conic bundle?
Hong-Jun Ge (TU)
On co-edge-regular graphs with four distinct eigenvalues
A connected graph is called co-edge-regular with parameters $(v,k,c)$ if it is $k$-regular and any two distinct vertices have exactly $c$ common neighbors. Tan-Koolen-Xia conjectured that connected co-edge-regular graphs with exactly four distinct eigenvalues and fixed smallest eigenvalue, when having sufficiently large valency, belong to two different families of graphs. In this talk, we focus on co-edge-regular graphs with exactly four distinct eigenvalues and present some counterexamples of Tan-Koolen-Xia conjecture, demonstrating that this class of graphs exhibits far more diverse behavior than previously expected. In particular, we show that even co-edge-regular graphs that are cospectral with the $2$-clique extension of a Latin square graph with smallest eigenvalue $-3$ are not determined by their spectrum.
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