(DMAT) Received June 20, 2023. The natural world is full of large systems of interacting units. A human brain, for example, contains around 86 billion (86 · 10^{9}) neurons whose activities evolve in time as a function …

(School of Mathematics, Birmingham). Received on 8/2/2023. In this note we will introduce the concept of character variety in the simple example of a torus with one disk removed. We will show how this is a surface …

(Instituut-Lorentz, Leiden). Received on 4/12/2022. Quantum mechanics allows for correlations that cannot be explained within two principles that are fundamental to our intuitive understanding of the world: locality and realism [1]. This led to Einstein and collaborators …

(DMAT, IMTech). Received on 21 November, 2022. Motivation: the conjecture of Birch and Swinnerton-Dyer In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute proposed seven challenges and one of these is the conjecture …

(DMAT, IMTech, CRM). Received 23 July, 2022. The paper [7] (see also [8]) solves a version of the Arnold diffusion problem for Hamiltonian systems that remained open since the 1960s. Hamiltonian systems appear naturally as models of …

(FWO-KU Leuven) Received 21 April, 2022. The paper [3] solves a long-standing conjecture about the structure of the roots of the Bernstein-Sato polynomial for plane branches posed by T. Yano in 1982 [18]. Let f : (C^{n+1}, …