Dynamic, stochastic systems exhibit a tremendously rich phenomenology including phase transitions and pattern formation. The equilibrium notions of universality and the laws of thermodynamics have to be extended to capture the evolution of systems appropriately. How this can be achieved is part of my research. Here, I use field-theories because in the past, they have been by far the most successful tool for understanding universality. Yet, these
non-equilibrium field theories are also interesting in their own right as a mathematical machinery to solve partial differential equations (PDEs). I want to come up with a dictionary that can tell you what phase transitions and
universality mean for PDE theory, and what shock waves imply for field theoretic descriptions.
Naturally, such systems have a zoo of applications in biology, neuroscience, finance and beyond. It is exciting for me to discover the connections between theory and real world systems and I try to keep my learning curve nice and steep.
Henry Philpott College Lecturer in Mathematics; Director of Studies
Johannes Pausch is a Teaching and Research Fellow in Mathematics. Before joining St Catharine’s, he was a Doctoral Prize Fellow at Imperial College London, where he also completed his PhD in Applied Mathematics. He holds a MASt in Physics from the University of Cambridge, a Master in Mathematics from UPMC Paris VI, and BSc.s in Physics and Mathematics from TU Berlin. He was born and raised in Dresden, Germany.