201 citations · 2.4k across the 113 of their papers we have counts for
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The Magnus expansion and Post-Lie algebras
Charles Curry, Kurusch Ebrahimi-Fard, Brynjulf Owren
We relate the classical and post-Lie Magnus expansions. Intertwining algebraic and geometric arguments allows to placing the classical Magnus expansion in the context of Lie group…
A group-theoretical approach to conditionally free cumulants
Kurusch Ebrahimi-Fard, Frederic Patras
In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cum…
Combinatorial Hopf algebra for interconnected nonlinear systems
Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
A detailed expose of the Hopf algebra approach to interconnected input-output systems in nonlinear control theory is presented. The focus is on input-output systems that can been r…
Planarly branched rough paths and rough differential equations on homogeneous spaces
Charles Curry, Kurusch Ebrahimi-Fard, Dominique Manchon +1
The central aim of this work is to understand rough differential equations on homogeneous spaces. We focus on the formal approach, by giving an explicit expansion of the solution a…
Quasi-shuffle algebras and renormalisation of rough differential equations
Yvain Bruned, Charles Curry, Kurusch Ebrahimi-Fard
The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on roo…