Rosa Lili Dora Preiß is a researcher and principal investigator in the transregional research cluster TRR 388 on Rough Analysis, Stochastic Dynamics and Related Fields. Together with Carlos Améndola and Bernd Sturmfels, she leads project A04 on Algebra and Geometry of Path Signatures. The team of A04 furthermore includes PostDoc Leonard Schmitz and PhD student Felix Lotter.
Her current university affiliation is with Technische Universität Berlin (TU Berlin) in the working group on Algebraic and Geometric Methods in Data Analysis.
Research interests
- Algebraic geometry of paths
- Iterated-integral signatures, rough paths and regularity structures
- Algebraic tools in stochastic analysis and mathematical physics
- Renormalisation procedures and the amplituhedron
- Invariant theory
- Category theory and Operads
- Machine learning and data science
Students
Felix Lotter (PhD student, since 2024, joint with Bernd Sturmfels)
Preprints
Joscha Diehl, Rosa Preiß and Jeremy Reizenstein. Conjugation, loop and closure invariants of the iterated-integrals signature. December 2024. arXiv:2412.19670 [math.RA]
Felix Lotter and Rosa Preiß. Cyclic polytopes through the lens of iterated integrals. To appear in Le Matematiche, special issue on Positive Geometry. arXiv:2412.11283 [math.RA]
Rosa Preiß. An algebraic geometry of paths via the iterated-integral signature. November 2023. arXiv:2311.17886 [math.RA].
Joscha Diehl, Terry Lyons, Rosa Preiß and Jeremy Reizenstein. Areas of areas generate the shuffle algebra. July 2021. arXiv:2002.02338 [math.RA].
Publications
Cristopher Salvi, Joscha Diehl, Terry Lyons, Rosa Preiß and Jeremy Reizenstein. A structure theorem for streamed information. Journal of Algebra, Volume 634, November 2023. doi:10.1016/j.jalgebra.2023.07.024.
Carlo Bellingeri, Peter K. Friz, Sylvie Paycha and Rosa Preiß. Smooth rough paths, their geometry and algebraic renormalization. Vietnam Journal of Mathematics, Volume 50, June 2022. doi:10.1007/s10013-022-00570-7.
Joscha Diehl, Rosa Preiß, Micheal Ruddy and Nikolas Tapia. The moving frame method for iterated-integrals: Orthogonal invariants. Foundations of Computational Mathematics, Volume 23, June 2022. doi:10.1007/s10208-022-09569-5
Laura Colmenarejo and Rosa Preiß. Signatures of paths transformed by polynomial maps. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Volume 61, Issue 4, Pages 695–717, December 2020. doi:10.1007/s13366-020-00493-9.
Yvain Bruned, Ilya Chevyrev, Peter K. Friz and Rosa Preiß. A rough path perspective on renormalisation. Journal of Functional Analysis, Volume 277, Issue 11, 108283, December 2019. doi:10.1016/j.jfa.2019.108283.