Project and Master Theses for Kurusch Ebrahimi-Fard

My research aims at developing mathematical methods useful to science and engineering. Topics of my work range from geometric integration methods, to nonlinear control theory, to Voiculescu’s free probability theory, to perturbative quantum field theory. Algebraic and combinatorial structures on graphs, partitions and other combinatorial objects are central in this respect. Currently, I am mainly interested in problems in nonlinear control theory, numerical analysis of ordinary and stochastic differential equations, and free probability theory. I am also working on various aspects of multiple zeta values and related topics.

Stochastic Calculus: solutions of matrix‐valued stochastic differential equations

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Nonlinear Control Theory: system interconnections, Faà di Bruno Hopf Algebra for feedback; Poincaré's center problem; Abel equations

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Free Probability: moment-cumulant relations from a shuffle Hopf algebraic point of view

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Numerical Integration Methods: pre- and post-Lie algebraic aspects; Magnus type expansions; order theory

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2016-12-12, Kurusch Ebrahimi-Fard