The Willmore ConjectureJahresbericht der Deutschen Mathematiker-Vereinigung - Tập 116 - Trang 201-222 - 2014
Fernando C. Marques, André Neves
The Willmore conjecture, proposed in 1965, concerns the quest to find the best
torus of all. This problem has inspired a lot of mathematics over the years,
helping bringing together ideas from subjects like conformal geometry, partial
differential equations, algebraic geometry and geometric measure theory. In this
article we survey the history of the conjecture and our recent solution through
the ... hiện toàn bộ
The Modular Isomorphism Problem: A SurveyJahresbericht der Deutschen Mathematiker-Vereinigung - - 2022
L. Margolis
AbstractThe Modular Isomorphism Problem asks if an isomorphism of group algebras
of two finite$p$p-groups$G$Gand$H$Hover a field of characteristic$p$p, implies
an isomorphism of the groups$G$Gand$H$H. We survey the history of the problem,
explain strategies which were developed to study it and present the recent
negative solution of the problem. The problem is also compared to other
isomorphism pr... hiện toàn bộ
The Singularity Theorems of General Relativity and Their Low Regularity ExtensionsJahresbericht der Deutschen Mathematiker-Vereinigung - - 2022
Roland Steinbauer
On the occasion of Sir Roger Penrose’s 2020 Nobel Prize in Physics, we review
the singularity theorems of General Relativity, as well as their recent
extension to Lorentzian metrics of low regularity. The latter is motivated by
the quest to explore the nature of the singularities predicted by the classical
theorems. Aiming at the more mathematically minded reader, we give a pedagogical
introductio... hiện toàn bộ
Vorwort Heft 1-2011Jahresbericht der Deutschen Mathematiker-Vereinigung - Tập 113 - Trang 1-2 - 2010
Hans-Christoph Grunau
Topological Insulators from the Perspective of Non-commutative Geometry and Index TheoryJahresbericht der Deutschen Mathematiker-Vereinigung - Tập 118 - Trang 247-273 - 2016
Hermann Schulz-Baldes
Topological insulators are solid state systems of independent electrons for
which the Fermi level lies in a mobility gap, but the Fermi projection is
nevertheless topologically non-trivial, namely it cannot be deformed into that
of a normal insulator. This non-trivial topology is encoded in adequately
defined invariants and implies the existence of surface states that are not
susceptible to Anders... hiện toàn bộ