There are seven questions in pure mathematics deemed important enough by the Clay Mathematics Institute, a nonprofit foundation devoted to “furthering the

That further restricts the freedom of China’s most influential tech talent — a category that encompasses entrepreneurs, researchers and executives.

In an earlier paper, M. Talagrand made a number of daring conjectures. An AI model provided a very beautiful proof of one of them which we explain here.

Security service says academics should stop taking grants from and working with firm backed by China’s intelligence service

In December 2024, we ran a survey about the future of AI, reaching 1,580 researchers internationally who had published at any of six leading artificial intelligence (AI) venues, corresponding to a 10% response rate...

Members of the University and Colleges Union are walking out in part of a long-running dispute over job and course cuts.

The University of Nottingham said it was "disappointed" by the timing of industrial action.

2 x full time, 3-year fixed term positions, located on the Camperdown Campus at the School of Mathematics and Statistics Opportunity to drive research in computational pure mathematics through the dev...

The Sylvester simplex $\mathsf{Sylv}_d^k$ is a $d$-dimensional lattice simplex with exactly $k$ interior lattice points. Sylvester simplices are conjectured to be the volume maximizers among all $d$-d...

Purpose: Assessing grant applications is time-consuming and difficult, adding to the overall burden of academic peer review. Whilst funders are exploring whether AI can help, there is no published res...

YouTube video by Institut Henri Poincaré

Gedeon, Proudfoot, and Young first conjectured that the graded Sn -representations H∙(Conf(n,Rd);Q) are strongly equivariantly log concave for even d. Later work of Matherne, Miyata, Proudfoot, and...

Let $k$ be a field of characteristic $p>0$. We prove that $m$ points and $n$ lines in $k^2$ determine $O((mn)^{2/3}+m+n+mn/p)$ incidences. In characteristic zero the last term is omitted. The proof us...

For an isolated hypersurface singularity f:(\CC^n,0_\rightarrow(\CC,0), we study the Łojasiewicz exponent ł(f) of f. We formulate three conjectures concerning: (i) attainment of ł(f) on coordinate polar curves, (ii) topological invariance of ł(f), and (iii) a local Newton-diagram formula for ł(f) in the Kushnirenko non-degenerate case. We compute ł(f) for all singularities of modality at most 2 in Arnold’s list and for several further families, obtaining systematic evidence in favor of these conjectures. We also find to what extent the collection of numerical invariants {modality⁡(f),ł(f),\mu(f),corank⁡(f),stabord⁡(f)} determines the stable equivalence class of f for the aforementioned singularities.

We establish a higher-dimensional irrationality criterion for periods which are presented as Mellin integrals depending on many parameters. The criterion is stated as an upper bound on the multi-variate transfinite diameter of the image of the domain of integration under the Mellin arguments. Most of the paper is devoted to studying notions of transfinite diameter relative to very general multivariate Vandermonde matrices. As a proof of principle, we illustrate how this approach works with detailed computations in the case of a 5-parameter family of integrals for \zeta(2) on \mathcal{M}_{0,5}, the moduli space of curves of genus 0 with 5 marked points. This yields a “higher-dimensional” proof of the irrationality of \zeta(2), based on an upper bound for a certain kind of transfinite diameter associated to \mathcal{M}_{0,5}.

Built in 1969, the Grade II* listed status Maths Houses won the 1970 RIBA Architecture Award. Designed by Bill Howell, with distinctive curved walls and integrated blackboards. Look around, draw on…

Built in 1969, the Grade II* listed status Maths Houses won the 1970 RIBA Architecture Award. Designed by Bill Howell, with distinctive curved walls and integrated blackboards. Look around, draw on…

Karim Adiprasito completed his undergraduate studies at TU Dortmund in 2010. He obtained a Ph.D. from Free University Berlin in 2013, under the supervision of Gunter M. Ziegler. He has been an Assistant Professor at the Einstein Institute for Mathematics Hebrew University of Jerusalem since 2015, promoted to full professor in 2018. Professor Adiprasito has given numerous invited talks in conferences and seminars. He received several prizes, for example, European Prize in Combinatorics, in 2015, for his work in discrete geometry; New Horizons Prize for Early-Career Achievement in Mathematics, associated with the Breakthrough Prize in Mathematics, in 2019; Prize of the European Mathematical Society in 2020, and is the 2021 Hadamard Lecturer.

Kawamata bounds for Fano threefolds and the Graded Ring Database - Volume 261