Lecturer: Dr. Rosa Preiß
Lecture: Wed 12:15-13:45 MA 549
Exercise class: Tue 10:15-11:45 MA 550
Note: If you can't make it to the exercise class, the lecture can also be taken without it if you do preparation and follow-up work for the lecture carefully on your own. However, if you can make it, the exercise class is recommended to help you with that, provide space to discuss your questions in great detail, and actually save you time in comparison to self-study!
Topics:
Lebesgue Stieltjes Integration, Riemann Stieltjes Integration, Sewing lemma, Young integration, Shuffle algebra, concatenation product and coproducts, Free Lie group, Iterated integrals, Chen's identity and the halfshuffle integration relation, characterization of paths up to tree-like equivalence, Chen-Chow theorem, Linear equivariance and invariants under rotation-reflection
Recommended prior knowledge: Linear Algebra I-II and Analysis I-III suffice!
Literature:
I will publish LaTeX notes regularly here. The following works can help your self-study:
Heinz Bauer: Maß- und Integrationstheorie. Or the english translation by Robert Burckel, Measure and Integration theory.
Tom Apostol: Mathematical Analysis, Chapter 7: The Riemann-Stieltjes Integral
Peter Friz, Nicolas Victoir: Multidimensional Stochastic Processes as Rough Paths: Theory and Applications
Ilya Chevyrev, Andrey Kormilitzin: A Primer on the Signature Method in Machine Learning
Christophe Reutenauer: Free Lie Algebras
Rosa Preiß: From Hopf algebras to rough paths and regularity structures
WiSe25/26 course of the module "Interdisciplinary topics in algebra, geometry, analysis, stochastics":
- Trainer/in: Carlos Enrique Améndola Cerón
- Trainer/in: Rosa Preiß