Critical processes on curved and dynamically evolving manifolds

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With the proposed project we would like to investigate equilibrium and in particular non-equilibrium critical phenomena in non-conventional geometries. One focus is the study of critical phenomena on background geometries with curvature. Here the main questions are how the curvature affects the critical behavior, how such systems can be treated both numerically and analytically, and how boundary conditions can be handled appropriately. In addition we intend to study various critical phenomena on dynamically evolving backgrounds. Here the simplest scenario would be a self-inflating or contracting flat space. The aim is to find out how the critical properties depend on the expansion/contraction characteristics. Moreover, it is challenging to implement well-known models with second-order phase transitions numerically in a setup where a regular static lattice cannot be used. Finally, it would be interesting to develop suitable field-theoretical approaches to deal with critical phenomena on dynamically evolving background geometries.