Mathematicians working at the computational forefront of algebra, geometry, and combinatorics gathered in Durham earlier this month for MEGA 2026 (Effective Methods in Algebraic Geometry), one of the world's leading conferences in computational algebraic geometry. The event, held from 6–10 July, marked the 19th edition of the prestigious biennial conference series and only the second time it has taken place in the UK.
Founded in 1990, MEGA has become the leading European conference on constructive and computational techniques in algebraic geometry. The field combines deep theoretical mathematics with powerful computational methods, with applications ranging from classical algebraic problems to modern challenges in areas such as structural rigidity, statistics and chemical reaction networks.
Hosted by Durham University's Department of Mathematical Sciences, the conference brought together established researchers and emerging scholars to share recent advances, discuss new computational tools and explore future directions for the subject.
The programme featured plenary lectures from nine internationally recognised speakers from across Europe and North America: Elisenda Feliu (University of Copenhagen), Tommy Hofmann (University of Siegen), Dimitra Kosta (University of Edinburgh), Khazhgali Kozhasov (Côte d'Azur University), Josef Schicho (Johannes Kepler University Linz), Alexandra Seceleanu (University of Nebraska-Lincoln), Anna Seigal (Harvard University), Liam Solus (KTH Royal Institute of Technology), Michael Walter (LMU Munich).
Alongside the plenary talks, participants took part in parallel sessions covering topics such as computational commutative algebra, real algebraic geometry, polynomial optimisation, tensor decompositions, algebraic statistics, combinatorial and toric algebra, and quantum-inspired applications. The week also included software demonstrations, a poster session and opportunities for collaboration and networking across the international research community.
It was a pleasure to welcome the MEGA community to Durham for a week of outstanding research in effective algebraic geometry. The feedback from participants has been fantastic, particularly regarding our venue and the inspiring views of Durham Cathedral. This year's gathering felt especially timely. For over three decades, the MEGA community has been leading the way in the healthy and effective use of computers in pure mathematics. Today, amidst the rise of LLMs and all the opportunities and uncertainties they bring, I am confident that our community will continue to set a standard for how we thoughtfully integrate these new tools going forward.
MEGA 2026 was supported by the UKRI Future Leaders Fellowship Programme, with additional support from the London Mathematical Society for UK-based PhD students. The successful hosting of MEGA 2026 reflects Durham's continuing strength in algebra, geometry and computational mathematics, while further strengthening the University's international research connections.
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