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Project A04
Project description
Project description
The signature of a path consists of tensors formed by iterated integrals, fundamental in rough path theory in stochastic analysis. This project investigates algebraic varieties arising from these signatures and their relation to Lie group structures. It aims to expand the interface between rough analysis and algebraic geometry. A focus is on exploring “signature varieties” in the context of Brownian motion mixtures and developing a non-commutative geometry of path signatures, with applications in computational geometry and statistical inference.
Principal Investigators
Principal Investigators
Carlos Améndola (TU Berlin)
Rosa Preiß (TU Berlin)
Bernd Sturmfels (MPI Leipzig)
Publications
Publications
Améndola, C., Galuppi, F., Ríos Ortiz, Á.D., Santarsiero, P., Seynnaeve, T., 2025. Decomposing tensor spaces via path signatures. Journal of Pure and Applied Algebra 229, 107807. https://doi.org/10.1016/j.jpaa.2024.107807 (projects A04, B01)
Publication prior to this CRC relevant to the project
Publication prior to this CRC relevant to the project
Bellingeri, C., Bruned, Y., Chevyrev, I., Preiß, R., 2024. Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields. Oberwolfach Rep. 20, 3063–3102. https://doi.org/10.4171/owr/2023/54
Preprints
Preprints
Diehl, J., Ibraheem, R., Schmitz, L., Wu, Y., 2025. Tensor-to-Tensor Models with Fast Iterated Sum Features. https://doi.org/10.48550/ARXIV.2506.06041
Schmitz, L., Wack, M., 2025. Finite Gröbner bases for quantum symmetric groups. https://doi.org/10.48550/ARXIV.2503.15104
Diehl, J., Preiß, R., Reizenstein, J., 2024. Conjugation, loop and closure invariants of the iterated-integrals signature. https://doi.org/10.48550/ARXIV.2412.19670
Lotter, F., Preiß, R., 2024. Cyclic polytopes through the lens of iterated integrals. https://doi.org/10.48550/ARXIV.2412.11283 (latest version may 2025)
Lotter, F., Schmitz, L., 2024. Signature matrices of membranes. https://doi.org/10.48550/ARXIV.2409.11996
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