Cluster algebras were developed by Fomin and Zelevinsky about twenty years ago. While the initial motivation came from within algebra (total positivity, canonical bases), it quickly became clear that cluster algebras ...

A Dirichlet form $\mathcal{E}$ is a densely defined bilinear form on a Hilbert space of the form $L^2(X,\mu)$, subject to some additional properties, which make sure that $\mathcal{E}$ can be considered as a natural ...

Finite element methodologies dominate the computational approaches for the solution to partial differential equations and nonstandard finite element schemes most urgently require mathematical insight in their design. The ...

Singularity theory concerns local and global structure of singularities of (algebraic) varieties and maps. As such, it combines tools from algebraic geometry, complex analysis, topology, algebra and combinatorics.

The classical theory of electromagnetism describes the interaction of electrically charged particles through electromagnetic forces, which are carried by the electric and magnetic fields. The propagation of the electromagnetic ...

Statistics for stochastic differential equations (SDEs) attempts to use SDEs as statistical models for real-world phenomena. This involves an understanding of qualitative properties of this class of stochastic processes ...