Alexander Engel – Page 2

Crafoord Prize 2024

The Crafoord Prize is awarded since 1982 by the Royal Swedish Academy of Sciences and the Crafoord Foundation. It is awarded in the categories mathematics and astronomy, geosciences, biosciences and polyarthritis (Holger Crafoord suffered from this disease). The Crafoord Prize in Mathematics 2024 is awarded to Claire Voisin “for outstanding contributions to complex and algebraic … Continue reading

An Olympiad-level AI system for geometry

The International Mathematical Olympiad (IMO) announced a few months ago the AIMO Prize: 5 million USD to the first AI that can win a gold medal! At least in geometry, this seems to be already in reach: Google DeepMind developed an AI-system that can solve in a benchmarking test 25 of 30 Olympiad geometry problems … Continue reading

A new lower bound for sphere packing

Recall that the classical sphere packing problem is the following: What is the maximum proportion of \(\mathbb{R}^d\) that can be covered by a collection of non-overlapping spheres of volume \(1\)? The exact value of this maximum is only known in dimensions 1, 2, 3, 8 and 24; and the cases 8 and 24 were only … Continue reading

Lotterien in Antragsverfahren

Heute kam die Ankündigung, dass die Stiftung Innovation in der Hochschullehre im Februar wieder eine Freiraum-Förderung ausschreiben wird (hier ein Link zu dem Blogbeitrag über die vorhergehende solche Förderung). Hierbei wird wieder, wie auch beim letzten Mal, zuerst eine Lotterie stattfinden, welche rein auf Glück eine gewisse Anzahl von Antragsskizzen durchlässt zum eigentlichen Verfahren. Die … Continue reading

Non-trivial units of complex group rings

One of most important mathematical results from 2021 was Gardam’s refutation of the unit conjecture (blog post): He constructed the first non-trivial unit in a group ring. The coefficients of the group ring of the first counter-example were \(\mathbb{F}_2\), and for three years the question whether one can generalize his idea to get counter-examples in … Continue reading

Pseudo-isotopies of 4-manifolds

One of the landmark results about the topology of 4-manifolds is Freedman’s proof of the 4-dimensional Poincaré conjecture. The problem with this result was that after some time people claiming to understand its proof disappeared, so that in the last decade the validity of this result was openly questioned (e.g., link). In the end, a … Continue reading

Formalizations in LEAN

I already blogged a few times about computer assisted verification of proofs, for example here: link. It seems to me that this topic is accelerating fast right now, especially formalizations in LEAN. In addition to the example linked above (a verification of a recent result of Clausen-Scholze), an important new result in combinatorics was recently … Continue reading

Freiraum 2023

Letztens wurden die Projekt verkündet, welche bei Freiraum 2023 gefördert werden. Im Rahmen von Freiraum können Mittel für die Verwirklichung von Projekten in der Lehre beantragt werden, und ich hatte mich diesmal gefragt, ob es etwas spannendes aus der (reinen) Mathematik darunter gibt. Da es keine Auflistung nach Fächern gibt, arbeitete ich mich durch die … Continue reading