A Course on Rough Paths

@inproceedings{Friz2014ACO,
  title={A Course on Rough Paths},
  author={Peter K. Friz and Martin Hairer},
  year={2014}
}
We give a short overview of the scopes of both the theory of rough paths and the theory of regularity structures. The main ideas are introduced and we point out some analogies with other branches of mathematics. 1.1 Controlled differential equations Differential equations are omnipresent in modern pure and applied mathematics; many “pure” disciplines in fact originate in attempts to analyse differential equations from various application areas. Classical ordinary differential equations (ODEs… 
Controlled Rough Paths on Manifolds I
TLDR
A theory of push-forwards is presented and it is shown that the integration of a smooth one-form along a manifold valued controlled rough path is in fact well defined independent of any additional geometric structures.
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References

Introduction to KPZ
This is an introductory survey of the Kardar-Parisi-Zhang equation (KPZ). The first chapter provides a non-rigorous background to the equation and to some of the many models which are supposed to lie