COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Why B-series, rooted trees, and free algebras? - 2

## Why B-series, rooted trees, and free algebras? - 2Add to your list(s) Download to your calendar using vCal - Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology)
- Tuesday 09 July 2019, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. GCSW01 - Tutorial workshop “We regard Butcher’s work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results”. This quote by Alain Connes summarises nicely the mathematical depth and scope of the theory of Butcher's B-series. The aim of this joined lecture is to answer the question posed in the title by drawing a line from B-series to those far-reaching conceptional results they originated. Unfolding the precise mathematical picture underlying B-series requires a combination of different perspectives and tools from geometry (connections); analysis (generalisations of Taylor expansions), algebra (pre-/post-Lie and Hopf algebras) and combinatorics (free algebras on rooted trees). This summarises also the scope of these lectures. In the first lecture we will outline the geometric foundations of B-series, and their cousins Lie-Butcher series. The latter is adapted to studying differential equations on manifolds. The theory of connections and parallel transport will be explained. In the second and third lectures we discuss the algebraic and combinatorial structures arising from the study of invariant connections. Rooted trees play a particular role here as they provide optimal index sets for the terms in Taylor series and generalisations thereof. The final lecture will discuss various applications of the theory in the numerical analysis of integration schemes. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsNew Directions in the Study of the Mind CAS FPGA Talks Cambridge Area Sequencing Informatics Meeting VII (2015)## Other talksBabraham Distinguished Lecture - "Control of B cell immunity and leukemia by the transcription factor Pax5" Trust & Technology Initiative 2019 Symposium Scaling populations and communities The Enigma of Emotion Classical Heredity in the Roman and Medieval Worlds (Domestication Practices across History) Cellular signalling networks in colon cancer and the models to study them. A basic research perspective |