Basic Science Lifetime Award in Mathematics 2025

After the Abel Prize and the Breakthrough Prizes the next ones in line are the Basic Science Lifetime Awards. In 2025 in the category mathematics they were awarded to Shigefumi Mori for his fundamental contributions to algebraic geometry, the Minimal Model Program, and profound influence in the classification of higher-dimensional algebraic varieties and to George … Continue reading "Basic Science Lifetime Award in Mathematics 2025"

Breakthrough Prizes 2025

Recently the Breakthrough Prizes were awarded (press release). The Breakthrough Prize in Mathematics 2025 goes to Dennis Gaitsgory for his central role in the proof of the geometric Langlands conjecture. The New Horizons in Mathematics Prizes go to Ewain Gwynne for his work in conformal probability, John Pardon for producing a number of important results … Continue reading "Breakthrough Prizes 2025"

Abel Prize 2025

The Abel Prize 2025 is awarded to Masaki Kashiwara for his fundamental contributions to algebraic analysis and representation theory, in particular the development of the theory of D-modules and the discovery of crystal bases.

The \(S^1\)-Stability Conjecture in Dimension 4

Last December I blogged about the \(S^1\)-stability conjecture for psc-metrics (link). Unfortunately, the result I explained there turned out to be wrong: Counter-examples can be found in dimension 4. Dimension 4 is special in the theory of psc-metrics since here one can use Seiberg-Witten theory to find obstructions to the existence of psc-metrics on closed … Continue reading "The \(S^1\)-Stability Conjecture in Dimension 4"

Optimality of Gerver’s Sofa

The moving sofa problem is one of those deceptively simple yet incredibly difficult “real-world” math problems. Despite its straightforward formulation, it has remained unsolved for roughly 60 years—until recently, when Jineon Baek announced a complete solution (arXiv:2411.19826; hopefully, this time the topic I’m blogging about won’t turn out to be incorrect in the end). In … Continue reading "Optimality of Gerver’s Sofa"

The \(S^1\)-Stability Conjecture for psc-Metrics

Jonathan Rosenberg introduced the following conjecture: A closed manifold \(M\) admits a Riemannian metric of positive scalar curvature if and only if the product \(M \times S^1\) admits one. One direction of the conjecture is trivial: If \(M\) admits a psc-metric, then the product metric on \(M \times S^1\) will also have psc. The other … Continue reading "The \(S^1\)-Stability Conjecture for psc-Metrics"