2024 Breakthrough Prize in Mathematics

The 2024 Breakthrough Prize in Mathematics goes to Simon Brendle for transformative contributions to differential geometry, including sharp geometric inequalities, many results on Ricci flow and mean curvature flow and the Lawson conjecture on minimal tori in the 3-sphere. The 2024 New Horizons in Mathematics Prize goes to Roland Bauerschmidt for outstanding contributions to probability … Continue reading "2024 Breakthrough Prize in Mathematics"

The Kervaire Conjecture

Think about your favourite non-trivial group. Now add a generator to it and then add any relation. Is the resulting group still non-trivial? The above question is known as the Kervaire conjecture. Phrased more concretely, if \(G\) is any non-trivial group and \(r \in G \ast \mathbb{Z}\), is \((G \ast \mathbb{Z})/\langle\!\langle r\rangle\!\rangle\) again non-trivial? This … Continue reading "The Kervaire Conjecture"

Shaw Prize 2023 in Mathematical Sciences

The Shaw Prize this year is awarded to Vladimir Drinfeld and Shing-Tung Yau for their contributions related to mathematical physics, to arithmetic geometry, to differential geometry and to Kähler geometry. More information can be found here: link.