QMUL Centre for Combinatorics, Algebra and Number Theory News

Welcome to Peter McNamara

Wed, 23 Sep 2026 23:00:00 GMT

We are pleased to be hosting Peter McNamara for a year-long visit as part of his sabbatical from Bucknell University. We asked him to tell us a bit about himself and his work. Tell us about your academic journey so far. Following undergrad at Trinity College Dublin, I did my Ph.D. at Massachusetts Institute of Technology. Both Federico Ardila and I had Richard Stanley as our advisor and graduated in 2003. After postdocs at Université du Québec à Montréal and at Instituto Superior Técnico in Lisbon, I joined Bucknell University in central Pennsylvania in 2006, and was promoted to full professor in 2017. What are you hoping to get out of your visit to Queen Mary? There's nobody else at Bucknell who does discrete math, so I'm looking forward to interacting with Centre members with overlapping interests. There is also great potential here for exploring avenues that are mostly new to me, especially tropical geometry and matroid theory. More broadly, I'm hoping to expand my network in the London area and in the UK in general. Overall, it's exciting to be able to devote so much time to research, something that gets very little of my time during a normal semester. What general area is your research in? Algebraic combinatorics, typically with more emphasis on the combinatorics side of this field. I've done projects focussed on partially ordered sets, bijective combinatorics, and, most extensively, symmetric and quasisymmetric functions. For the algebra of symmetric functions, the most studied basis is the Schur functions, due to their beautiful combinatorial definition in terms of Young tableaux, and because they arise in other areas of pure mathematics, including representation theory, Schubert calculus, and eigenvalues of matrices. Over the years, Schur functions have been extended in many directions but perhaps the simplest generalisation are the skew Schur functions. The skew Schur functions are too numerous to form a basis, and I've written several papers examining the relations among skew Schur functions. And could you tell us something about a specific problem you have worked on? The Schur functions can be indexed by Young diagrams, and the skew Schur functions are indexed by skew Young diagrams. Is there a way to tell if two skew Schur functions are equal just by looking at their skew Young diagrams? Stephanie van Willgenburg and I devised the first conjectural necessary and sufficient conditions for two skew Young diagrams to yield the same skew Schur function. We proved one half of the sufficiency direction, and the other half was recently completed by Nick Olson-Harris; the necessary direction is wide open. What do you enjoy most about your area of maths? I like that it's often easy to get to concrete questions without knowing too much background. Many of the questions I study are amenable to conjecture generation and testing by computer. These two aspects, besides appealing to me, also make my area accessible to advanced undergraduates. What are your interests outside maths? Cycling, including optimizing my route to and from work among many choices. I spend an inordinate amount of time traveling to and watching my daughters' (aged 9 and 15) football trainings and practices, and I'm getting to know the suburbs of London quite well! On some other personal notes, my wife, Emily Dryden, works in spectral geometry and geometric analysis, and is spending the year at King's. By now, we've met people at work, schools and football, and have been impressed at how welcoming and accommodating everyone has been.

Summer research internships for undergraduate students

Fri, 12 Jun 2026 23:00:00 GMT

Ten talented undergraduate students from across a wide range of Science and Engineering programmes are embarking on exciting summer research internships under the mentorship of academic supervisors. This fantastic opportunity has been made possible through the QMUL Summer Training Research Initiative to Support Diversity and Equality (STRIDE) and the London Mathematical Society's Undergraduate Research Bursaries (URB) scheme. Spanning the full breadth of Science and Engineering, these diverse and innovative projects offer students a unique chance to explore research, develop new skills, and gain first-hand experience of academic discovery. We hope the programme will inspire the next generation of researchers and ignite a lasting passion for scientific inquiry. Below, you can find the full list of projects, students, and supervisors taking part in this year's programme. Zahra Ibrahim Ahmed Yusuf: An inclusive approach to measuring depression in neurodivergent young adults from diverse backgrounds (supervisor Giorgia Michelini) Tahran Tinnin Motlib-Siddiqui: Bioelectronic Sensors for Lanthanides (supervisor Lin Su) Radoslaw Bukowiński: LoRa-Based Satellite Ground Station Development and Link Analysis using the TinyGS Network (supervisor Fatma Benkhelifa) Mohammed Rizwan Miah: Offshore Aquaculture Renewables (supervisor Eldad Avital) Elsie Chidera Obiako: Developing AI tools for image-based diagnosis (supervisor Shaheer U Saeed) Amina Abulrahim Montalto: Domestic Water Recycling (supervisor Eldad Avital) Nursen Adiba Chowdhury: Synthesis, Fabrication and Characterization of Novel Antiferroelectric Materials (supervisor Giuseppe Viola) Ivet Lobo: Combinatorial search algorithms- AI and Machine Learning vs Integer Optimization (supervisor Thomas Prellberg) Zishan Xu: Higher order hyperbolic problems with singularities (LMS URB, supervisor Claudia Garetto) Oliver Leo Carter: Matroids that maximase a valuative invariant (LMS URB, supervisors Alex Fink and Mark Jerrum)

12 May: International Women in Mathematics Day

Sun, 10 May 2026 23:00:00 GMT

International Women in Mathematics Day is celebrated on 12 May, marking the birthday of Maryam Mirzakhani, the first woman to receive the Fields Medal in 2014. Born in Iran, Mirzakhani made groundbreaking contributions to mathematics before her life was cut short at a young age. Her legacy continues to inspire women and underrepresented groups in mathematics worldwide. This International Women in Mathematics Day we spotlight the research profile of two female colleagues in the School of Mathematical Sciences: Professor Ginestra Bianconi and Dr Miriam Norris. Ginestra Bianconi is Professor of Applied Mathematics in the Centre for Complex Systems. She is Fellow of the American Physical Society and member of the European Academy of Sciences for her work on statistical mechanics . In 2025, she was awarded the Euler Prize by the Network Science Society for her pioneering contributions revealing the interplay between the topology of networks and their dynamics. She is the author of the monograph Higher-Order Networks: An Introduction to Simplicial Complexes (Cambridge University Press, 2021). Her current research focuses on the establishing the deep mathematical relation between geometry, topology, and dynamics on higher-order networks. She uses algebraic topology to define the dynamical state of simplicial complexes, revealing new collective phenomena relevant to complex systems and theoretical physics. Over the past five years, she has promoted the use of the Topological Dirac operator to characterize the interplay between topology, geometry, and dynamics, and to explore its role in theoretical physics and dynamical systems. More recently, she has opened a new research direction in quantum gravity with the formulation of the Gravity from Entropy (GfE) approach which proposes an entropic action from gravity. You can read about this work here. Miriam Norris is a senior Heilbronn Research Fellow in the Centre for Combinatorics Algebra and Number Theory. Miriam's research is devoted to representation theory in the intersection between algebra and number theory. She is currently working with Dr Shu Sasaki on aspects of representation theory involved in the Langlands programme. Miriam returned to London from a postdoc in Manchester in October 2025 having done her PhD within the London School of Geometry and Number Theory. Outside of maths she really enjoys hiking and cycling around the city, particularly over London's bridges!

Professor Federico Ardila joining QMUL in January 2026

Thu, 11 Dec 2025 00:00:00 GMT

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