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Minicourse: Deterministic and Random Processes, Prof. Jens Lorenz.

Differential equations and difference equations are used to model deterministic processes in continuous and in discrete time. Some interesting phenomena are stability, bifurcations, and chaos. For chaotic processes, individual trajectories are typically ill--determined, but their average behavior may still be very well defined.

In this course we also want to learn about random evolution where a state u_n progresses to another state u_{n+1} with some probability p(u_n,u_{n+1}). We will then compare deterministic and random growth processes. It is also interesting to study the evolution from order to chaos via random evolution and to related this to irreversibility in time.

Prof. Lorenz is a faculty member in Applied Mathematics at UNM, whose research is in the area of Applied Analysis of partial differential equations and their numerical approximation. He is on the editorial board of four journals. He served as Graduate Chair (2010-2011), as Interim Department Chair (2008--2009), and as Associate Chair (2014--2015). He has mentored several sturents in our department's Undergraduate Research program. He has written a book, Deterministic and Random Evolution, which was published by Nova Science Publishers in 2013. This book is based on his lecture notes from the previously NSF funded MCTP workshops.