QMUL Centre for Combinatorics, Algebra and Number Theory News

Professor Federico Ardila joining QMUL in January 2026

Thu, 11 Dec 2025 00:00:00 +0100

Prof. Federico Ardila will be joining the School of Mathematical Sciences, QMUL in January 2026 as part of the Faculty of Science and Engineering Talent scheme. Ardila is a Colombian mathematician whose work in matroid theory lies at the intersection of combinatorics with geometry, algebra, topology, and applications. Apart from his research, Prof. Ardila is also widely known for his efforts to make the mathematical community more just, more equitable, and more welcoming, and for a set of of axioms that attempt to encapsulate these efforts. Among many possibilities, some highlights from his mathematical career include: Work with Klivans which gives a combinatorial description of the Bergman fan, providing new geometric insights into this fundamental object from algebraic geometry. This also led to a connection between these objects and phylogenetics, which has driven several important advances in algorithms for reconstructing phylogenies in mathematical biology. His contributions at the forefront of the revolution in modern matroid theory instigated by June Huh (2022 Fields medalist). In work with Denham and Huh he extended and strengthened the Hodge theoretic approach in ways that both answered two open problems from the 1980s and has allowed later work to use many different geometries, not only the 'wonderful compactification' that Huh employed. In 2022 he was an invited speaker at the International Congress of Mathematicians (the largest and most prestigious mathematics conference). He created and ran the SFSU–Colombia Combinatorics Initiative which through his innovative approach to graduate education launched many students into research. This scheme embodies his approach to diversify mathematics and resulted in a whole generation of Colombians working as early- to mid-career researchers worldwide as well as a very healthy combinatorics community inside the country. We look forward to Federico enriching Queen Mary with his mathematical expertise and his approach to doing mathematics. Ardila's Axioms Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries. Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences. Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs. Axiom 4. Every student deserves to be treated with dignity and respect. You can find out more about Federico and his research on his website: https://fardila.com Federico is also a regular contributor to the Numberphile project. You can find his contributions here: https://www.numberphile.com/videos/category/Federico+Ardila Or, for something more technical, his ICM talk and survey article "The geometry of geometries: matroid theory, old and new" is available to watch: https://www.youtube.com/watch?v=mrnB-SYaHZE or read: https://arxiv.org/abs/2111.08726

Welcome to Our New Postdocs

Sun, 05 Oct 2025 23:00:00 +0100

We welcome a bumper cohort of postdocs to the Centre for Combinatorics, Algebra and Number Theory this year. For this post, we asked them to introduce themselves and say a bit about their mathematical journey to QMUL and what they will be getting up to during their time here. Himanshi Chanana Hello, I am Himanshi Chanana, a postdoctoral researcher in mathematics at QMUL. I am originally from India and recently completed my PhD at the Indian Institute of Technology Kanpur, where I worked under the supervision of Prof. Saurabh Kumar Singh. My research lies in analytic number theory, an area of mathematics that seeks to understand deep questions about prime numbers. A famous example is the Riemann Hypothesis, which predicts hidden patterns in the distribution of primes. While my work does not directly address this problem, it contributes to the broader picture by studying automorphic forms and L-functions — central objects that are closely connected to many important questions in number theory. At QMUL, I am working on the project titled "Moments of Higher Rank L-functions" under the guidance of Subhajit Jana. Roughly speaking, this involves studying the average behaviour of L-functions. This often reveals surprising arithmetic insights connected with major conjectures such as the Generalized Lindelöf Hypothesis and subconvexity bounds. Right now, I am particularly focused on studying automorphic forms from a representation-theoretic viewpoint. I am excited to learn new techniques, explore different perspectives, and collaborate with others in this area. Patience Ablett Hi! I'm Patience, and I work in combinatorial algebraic geometry. During my PhD I got hooked on toric varieties, a special class of algebraic varieties whose geometry can be understood via combinatorics. During my time at QMUL I'll be continuing my work in this area with Alex Fink, as well as branching out into some matroid theory. Miriam Norris I am a representation theorist whose work lies in the intersection between algebra and number theory. After completing an undergraduate degree at the University of Edinburgh I joined the London School of Geometry and Number Theory. I graduated from Kings College London with a PhD in 2022 under the supervision of Prof Fred Diamond and Prof Martin Liebeck. Since then, I have been a research fellow at the University of Manchester and now QMUL where I will be working with Shu Sasaki. I am interested in representations of algebraic, p-adic and related finite groups. Specifically, I am interested in the aspects of representation theory involved in the Langlands programme. This programme aims to bridge two distinct areas of maths, harmonic analysis (automorphic forms) and number theory (Galois representations). The discovery of such `bridges' has proved extremely valuable with a notable example being part of Andrew Wiles' proof of Fermat's Last Theorem. Robin Bartlett I recently moved from Glasgow to take up an MSCA fellowship at QMUL where I will be working with Shu Sasaki. My academic work sits at the interface of representation theory and geometry: I study how representation-theoretic patterns can be realised inside geometric objects that arise in the Langlands program. In this project I'm particularly excited to explore new connections to geometric representation theory, and am looking forward to collaborating across the group. Outside of mathematics I enjoy painting and reading, which helps me take a step away from research and return to problems with a fresh viewpoint. We wish all of the new postdocs an extremely productive and enjoyable time at Queen Mary, and look forward to being part of the next steps in their mathematical careers! You can find more about them and their work on their websites: Himanshi Chanana Patience Ablett Dante Luber Robin Bartlett

Applied Algebra and Geometry Network Meeting Report

Wed, 01 Oct 2025 23:00:00 +0100

The School of Mathematical Sciences hosted the twenty-second meeting of the Applied Algebra and Geometry Network on Monday 15 September with a large contingent from the Centre for Combinatorics, Algebra and Number Theory participating. Queen Mary postdoc Dante Luber shared his thoughts after the meeting. What were your general impressions of the conference? All of the speakers made an effort not to assume too much background knowledge, and the material was presented in an accessible way. The talks were given at a relaxed pace and the speakers were receptive to questions. Between talks, there was a generally talkative atmosphere. There were lots of opportunities to catch up with people I already knew, and meet more people from the UK algebraic geometry community. How do you feel it has helped your research? The first talk [Primoz Skraba (QMUL), "Geometry and (Co)Homology Computation"] concerned cohomology computations. Cohomology has been coming up in my more recent research, and I am always interested in ways direct computation can be involved. Furthermore, it was interesting to hear about the algorithms the speaker introduced. I am curious if these could (or maybe have already been) implemented in software systems such as OSCAR. The second talk also touched on areas related to my work, as it considered group actions on algebraic varieties and the associated representation theory. The last talk concerned cryptography in tropical geometry. While my work in tropical geometry does not relate to cryptography, it was cool the broad range of problems the area can be applied to. If an undergraduate wanted to attend the conference, what advice would you give them? I would say that the most important part of any talk for a non-expert is the first half or so, where the speaker introduces the fundamental concepts and background which are prerequisite to understand their results. Don't worry about understanding all the details during the talk, but take notes on the big picture and key words. Later, you can go over those notes and find resources to fill in the details. Don't be afraid to approach the speakers between the talks to ask questions less to their results. I think it's perfectly fine to ask a speaker "what's a good resource if I wanted to learn about X", where X is a topic that came up in their talk. Also, there's no harm in asking a speaker to send you their slides. In fact, I did this for one of the talks at this meeting. Take a look at the Applied Algebra and Geometry Network website to find out more, including details of upcoming meetings and how to sign up for their newsletter.

EPSRC Grant Success: "Zeros, Algorithms, and Correlation for Graph Polynomials" led ...

Mon, 15 Sep 2025 23:00:00 +0100

An EPSRC standard grant has been awarded to Viresh Patel (Project Lead) and Mark Jerrum (Project Co-lead) for the project "Zeros, Algorithms, and Correlation for Graph Polynomials". Read on to find out more about their plans. This project is at the interface of theoretical computer science, mathematics and statistical physics. It aims to establish and leverage formal connections between different notions of phase transitions in these three different areas to make breakthroughs on long-standing questions. A phase transition is the phenomenon where a small change in some measure of a system (e.g. its temperature) results in a large change in its macroscopic behaviour (e.g. a material turning from a solid to a liquid). Phase transitions are currently at the forefront of study in several disciplines. We study phase transitions in spin systems. Spin systems are networks where each node is randomly placed in one of several possible states but where the states of neighbouring nodes tend to influence each other. These spin systems exhibit remarkably rich behaviours; they originate in statistical physics, where they model gases, magnetism and other physical phenomena, but they can also help explain complex group behaviours like voting (here the vote of an individual in a social network may be correlated with the votes of their neighbours). The partition function of a spin system is a polynomial that encodes much of the system's behaviour. A major goal in theoretical computer science and of this project is to develop fast algorithms to approximate these partition functions. The existence of such algorithms has recently been connected with the location of the zeros of partition functions, a topic of independent interest in mathematics and statistical physics since the 1950s. The project addresses several challenges here including that of understanding how strong spatial mixing for a spin system, that is the extent to which the state of a node influences the state at other distant nodes, affects the location of the zeros of its partition function. Some of the specific highlights of the project are to attack the intensely studied problem of finding a an approximation algorithm for counting proper colourings in graphs (a.k.a configurations in the zero-temperature antiferromagnetic Potts model), to understand the algorithmic behaviour of the hardcore model when the underlying graph has some structure, to develop deterministic algorithms for approximating the Ising and monomer-dimer models, and to do all of this by understanding the zeros of the partition function in each of these cases. We have an international project partner, Dr Guus Regts, at the University of Amsterdam, and there are several research visits planned in both directions between the groups at Queen Mary and Amsterdam, starting with PhaseCAP, a research semester programme at CWI, Amsterdam. We will also soon be advertising for a postdoc to join the project.