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Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry.

The main goal of this Methusalem research program is to bring together KU Leuven's leading researchers in pure mathematics to focus on some of the most challenging problems in algebra, analysis, and geometry, and their numerous interactions.This Methusalem research program has the following main goals:

  • Algebraic geometry. The goal is to uncover geometric properties of solution sets of algebraic equations. Combining different methods from arithmetic and algebraic geometry, we study problems in number theory, singularity theory and the birational classification of algebraic varieties, with a special focus on Calabi-Yau varieties and motivic integration.
  • Classical analysis. This part centers around eigenvalue distributions of random matrices. The main goal is to exhibit universality phenomena in the local eigenvalue correlations of large random matrices.
  • Differential geometry. We construct global, group-like objects associated to infinitesimal geometric structures such as singular foliations or Poisson spaces. The goal is to exploit the algebraic properties of the former to study the symmetries of these singular spaces.
  • Functional analysis. The dynamic and ergodic properties of discrete groups and their actions on probability spaces are captured by the associated algebras of operators on a Hilbert space. The main goal is to classify these von Neumann algebras coming from the free groups or from lattices in Lie groups.
  • Group theory. Infra-nilmanifolds are geometric objects that arise naturally in topology and dynamical systems. We study their geometric and topological properties through their associated nilpotent Lie algebras, resulting in applications for fixed point problems.
Date:1 Jan 2016 →  Today
Keywords:Classification, symmetries, singularities, algebra, analysis, geometry
Disciplines:Analysis, Applied mathematics in specific fields, General mathematics, History and foundations, Other mathematical sciences