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 thesisIf you are interested in doing a Master's thesis in the area of algebra, machine learning or statistics, please send me an email!ActivitiesSignatures for images, August 2023 - June 2024 Lecture Building blocks of modern machine learning, summer term 2023 Each Friday, at 15:00h, I co-organize an online seminar onAlgebra, Combinatorics and Perspectives in Mathematical Sciences. Please send me an email if you are interested in attending. I am the German PI in the ANR-DFG-JST funded, trilateral project EnhanceD Data stream Analysis with the Signature Method. I am a member of the international consortium Anthropological and Mathematical Analysis of Archaeological and Zooarchaeological Evidence. I co-organize a online reading group on decomposition spaces. Please send me an email if you are interested in participating. Makerspace Nano (in the premises of StartUP Zukunfswerft)Past events2022-06 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 The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures Shuffle Algebras and Non-Commutative Probability for Pairs of Faces with M. Gerhold and N. GilliersSIGMA, 2023.Half shuffle identities in arity 3 on Zinbiel and Tortkara algebras and a structure theorem for streamed information with C. Salvi, T. Lyons, R. Preiß and J. ReizensteinarXiv:2212.00134, 2022.Tropical time series, iterated-sums signatures and quasisymmetric functions(video, arxiv) with K. Ebrahimi-Fard and N. TapiaSIAM Journal on Applied Algebra and Geometry, 2022.Two-parameter sums signatures and corresponding quasisymmetric functions (video) with L. SchmitzarXiv:2210.14247, 2022.Graph counting signatures and bicommutative Hopf algebras with D. Caudillo, K. Ebrahimi-Fard and E. VerriarXiv:2206.08323, 2022.The moving frame method for iterated-integrals: orthogonal invariantswith R. Preiß, M. Ruddy and N. TapiaFoundations of Computational Mathematics, 2022.A quadratic identity in the shuffle algebra and a new proof for de Bruijn's formulawith L. Colmenarejo and M.-S. SoreaEuropean 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. KimJournal of Hand Therapy, 2021.Generalized iterated-sums signatureswith K. Ebrahimi-Fard and N. TapiaarXiv:2012.04597, 2020.Areas of areas generate the shuffle algebrawith T. Lyons, R. Preiß and J. ReizensteinarXiv:2002.02338, 2020.Iterated-sums signature, quasisymmetric functions and time series analysiswith K. Ebrahimi-Fard and N. TapiaSéminaire 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. TapiaActa Applicandae Mathematicae, 2020.The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergencewith H. Boedihardjo, M. Mezzarobba and H. NiBulletin of the London Mathematical Society, 2020.The parabolic Anderson model on Riemann surfaceswith A. Dahlqvist and B. DriverProbability Theory and Related Fields, 2019.Invariants of multidimensional time series based on their iterated-integral signaturewith J. ReizensteinActa Applicandae Mathematicae, 2018.Backward stochastic differential equations with Young driftwith J. ZhangProbability, Uncertainty and Quantitative Risk, 2017.The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric interacting Brownian motionswith M. Gubinelli and N. PerkowskiCommunications in Mathematical Physics, 2017.Stochastic partial differential equations: a rough paths view on weak solutions via Feynman-Kacwith P. Friz and W. StannatAnnales de la Faculté des Sciences de Toulouse, 2017.Stochastic control with rough pathswith P. Friz and P. Gassiat,Applied Mathematics & Optimization, 2016.Pathwise stability of likelihood estimators for diffusions via rough pathswith P. Friz and H. MaiThe Annals of Applied Probability, 2016.The inverse problem for rough controlled differential equationswith I. BailleulSIAM Journal on Control and Optimization, 2015.Regularity Theory for Rough Partial Differential Equations and Parabolic Comparison Revisitedwith P. Friz and H. OberhauserSpringer Proceedings in Mathematics & Statistics, 2014.A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough PDEswith H. Oberhauser and S. RiedelStochastic Processes and their Applications, 2014.Robustness in stochastic filtering and maximum likelihood estimation for SDEswith P. Friz, H. Mai, H. Oberhauser, R. Riedel and W. StannatExtraction of Quantifiable Information from Complex Systems, Springer, 2014.Robust Filtering: Correlated Noise and Multidimensional Observationwith D. Crisan, P. Friz and H. OberhauserAnnals of Applied Probability, 2013.Backward stochastic differential equations with rough driverswith P. FrizAnnals of Probability, 2012.

ProofsStone-Weierstraß theorem

Codehttps://github.com/diehlj