Singularity theory concerns local and global structure of singularities of algebraic varieties and maps, often focusing on the interplay between algebraic geometry, symplectic topology, algebra, combinatorics, etc.

Over the last 30 years, there has been spectacular progress in deriving the well-known hydrodynamic limits from stochastic interacting particle systems, as well as characterizing the fluctuations of locally conserved quantities ...

The theory of subfactors plays an important role in the discovery and analysis of quantum symmetries that seem to be ubiquitous in mathematics and physics. Subfactors profoundly interact with a wide range of different ...

Uncertainty quantification (UQ) is concerned with including and characterising uncertainties in mathematical models. Major steps include the proper description of system uncertainties, analysis and efficient quantification ...