Joscha Diehl I am a professor (W1) of Stochastic Analysis at the University of Greifswald. Email: first name . last name at gmail . com Office hours: send me an email to schedule a meeting. Master's thesis If you are interested in doing a Master's thesis in the area of algebra, combinatorics or machine learning, please send me an email! Activities Counting permutation and chirotope patterns (in the DFG priority programme SPP 2458 "Combinatorial Synergies") Every second Friday, at 15:00h, I co-organize an online seminar on Algebra, Combinatorics and Perspectives in Mathematical Sciences. Please send me an email if you are interested in attending. Makerspace Nano (in the premises of StartUP Zukunfswerft) Past events I was the German PI in the ANR-DFG-JST funded, trilateral project EnhanceD Data stream Analysis with the Signature Method. Mathematics of data streams: signatures, neural differential equations, and diffusion models Spring school and workshop, 8.4.-13.4.2024, Greifswald Signatures for images, August 2023 - June 2024 Lecture Building blocks of modern machine learning, summer term 2023 2022-06 Augmented reality and machine learning - Hackathon 7.6.-10.6.2022 2022-03 AR Programming Beginner Course (online; 5./6.03 and 12./13.03.22) 2021-09-20/-25 Noncommutative algebra, probability and analysis in action, Greifswald 2021-04-08 Special day on the amplituhedron. 2020-10-01 Talk (at datasig): Tropical time series, iterated-sums signatures and quasisymmetric functions 2020-09-02 Talk (at MPI for Mathematics in the Sciences, Leipzig): Convolutional neural networks for sequential data and tropical quasisymmetric functions. 2020-08-26 Talk (at RSS Applied Probability Section: Rough path theory in machine learning): Tropical quasisymmetric functions in time series analysis 2020-08-11/-14 Workshop: Geometry of curves in time series and shape analysis, August 11 - 14, 2020 2020-04-28 Talk (at Nonlinear Algebra Seminar Online, MPI for Mathematics in the Sciences, Leipzig): Time warping invariants and quasisymmetric functions 2019-11-14/15 Workshop: Algebraic and analytic perspectives in the theory of rough paths and signatures, November 14-15, 2019, Oslo. Publications -> on google scholar On a generalization of corner trees with E. Verri arXiv:2408.08293, 2024. A multiplicative surface signature through its Magnus expansion with I. Chevyrev, K. Ebrahimi-Fard, N. Tapia arXiv:2406.16856, 2024. On the signature of an image with K. Ebrahimi-Fard, F. Harang, S. Tindel arXiv:2403.00130, 2024. FRUITS: Feature Extraction Using Iterated Sums for Time Series Classification (github) with R. Krieg Data Mining and Knowledge Discovery, 2024. Hopf Algebra on Vincular Permutation Patterns with E. Verri arXiv:2306.17800, 2023. Generalized iterated-sums signatures with K. Ebrahimi-Fard and N. Tapia Journal of Algebra, 2023. The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures (arxiv) with M. Clausel, R. Mignot, L. Schmitz, N. Sugiura and K. Usevich SIAM Journal on Applied Algebra and Geometry, 2024 Shuffle Algebras and Non-Commutative Probability for Pairs of Faces with M. Gerhold and N. Gilliers SIGMA, 2023. A structure theorem for streamed information (arxiv) with C. Salvi, T. Lyons, R. Preiß and J. Reizenstein Journal of Algebra, 2023. Tropical time series, iterated-sums signatures and quasisymmetric functions (video, arxiv) with K. Ebrahimi-Fard and N. Tapia SIAM Journal on Applied Algebra and Geometry, 2022. Two-parameter sums signatures and corresponding quasisymmetric functions (video) with L. Schmitz arXiv:2210.14247, 2022. Graph counting signatures and bicommutative Hopf algebras with D. Caudillo, K. Ebrahimi-Fard and E. Verri arXiv:2206.08323, 2022. The moving frame method for iterated-integrals: orthogonal invariants with R. Preiß, M. Ruddy and N. Tapia Foundations of Computational Mathematics, 2022. A quadratic identity in the shuffle algebra and a new proof for de Bruijn's formula with L. Colmenarejo and M.-S. Sorea European Journal of Combinatorics, 2022. Increase of weight-bearing capacity of patients with lesions of the TFCC using a wrist brace with A. Asmus, M. Sallouma, W. Medeiros, M. Millrose, A. Obladen, L. Goelz, A. Eisenschen, A. Ekkernkamp and S. Kim Journal of Hand Therapy, 2021. Areas of areas generate the shuffle algebra with T. Lyons, R. Preiß and J. Reizenstein arXiv:2002.02338, 2020. Iterated-sums signature, quasisymmetric functions and time series analysis with K. Ebrahimi-Fard and N. Tapia Séminaire Lotharingien de Combinatoire 84B, 2020, Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics. Time warping invariants of multidimensional time series (video) with K. Ebrahimi-Fard and N. Tapia Acta Applicandae Mathematicae, 2020. The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence with H. Boedihardjo, M. Mezzarobba and H. Ni Bulletin of the London Mathematical Society, 2020. The parabolic Anderson model on Riemann surfaces with A. Dahlqvist and B. Driver Probability Theory and Related Fields, 2019. Invariants of multidimensional time series based on their iterated-integral signature with J. Reizenstein Acta Applicandae Mathematicae, 2018. Backward stochastic differential equations with Young drift with J. Zhang Probability, Uncertainty and Quantitative Risk, 2017. The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions with M. Gubinelli and N. Perkowski Communications in Mathematical Physics, 2017. Stochastic partial differential equations: a rough paths view on weak solutions via Feynman-Kac with P. Friz and W. Stannat Annales de la Faculté des Sciences de Toulouse, 2017. Stochastic control with rough paths with P. Friz and P. Gassiat, Applied Mathematics & Optimization, 2016. Pathwise stability of likelihood estimators for diffusions via rough paths with P. Friz and H. Mai The Annals of Applied Probability, 2016. The inverse problem for rough controlled differential equations with I. Bailleul SIAM Journal on Control and Optimization, 2015. Regularity Theory for Rough Partial Differential Equations and Parabolic Comparison Revisited with P. Friz and H. Oberhauser Springer Proceedings in Mathematics & Statistics, 2014. A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough PDEs with H. Oberhauser and S. Riedel Stochastic Processes and their Applications, 2014. Robustness in stochastic filtering and maximum likelihood estimation for SDEs with P. Friz, H. Mai, H. Oberhauser, R. Riedel and W. Stannat Extraction of Quantifiable Information from Complex Systems, Springer, 2014. Robust Filtering: Correlated Noise and Multidimensional Observation with D. Crisan, P. Friz and H. Oberhauser Annals of Applied Probability, 2013. Backward stochastic differential equations with rough drivers with P. Friz Annals of Probability, 2012.
Proofs Stone-Weierstraß theorem
Code https://github.com/diehlj