Dr. Nikolas Tapia
- Address: Mohrenstraße 39, 10117 Berlin, Germany.
- Office: Hausvogteiplatz 11, room 0.02
- Telephone: +49 30 20372-448.
- e-mail: lastname (at) FQDN of this page.
- Here is my PGP public key. Fingerprint:
- My CV.
I am part of the Stochastic Algorithms and Nonparametric Statistics research group at the Weierstraß Institute for Applied Analysis and Stochastics.
I work as a Postdoctoral Researcher in the MATH+ AA4-2 project "Optimal Control in Energy Markets Using Rough Analysis and Deep Networks", led by C. Bayer, P. K. Friz, John Schoenmakers, and Vladimir Spokoiny.
Previously, I was part of the Differential Equations and Numerical Analysis research group at the Norwegian University of Science and Technology, where I worked with K. Ebrahimi-Fard.
Before that, I obtained a joint PhD in Mathematics from the University of Chile and Sorbonne Université under the direction of D. Remenik and L. Zambotti.
📷 Geraldine Cossio, 2021.
- I co-organize the Algebraic and Combinatorial Perspectives in the Mathematical Sciences seminar (Fridays @ 15:00 CET).
- Robustness of Deep Neural Networks, with Christian Bayer, Simon Breneis, and Peter Friz.
- Pathwise Itô formula for branched Rough Paths, with Carlo Bellingeri and Emilio Ferrucci.
- Geometry of controlled paths, with Mazyar Ghani-Varzaneh, Sebastian Riedel, and Alexander Schmeding.
- Signature compression via tensor train formats, with Christian Bayer, Martin Eigel, and Robert Gruhlke.
- Translation of branched rough paths, with Joschal Diehl, Kurusch Ebrahimi-Fard, and Rosa Preiß.
Preprints and Publications
Articles in Refereed Journals
- C. Bayer, P. K. Friz, N. Tapia. Stability of deep Neural Networks via discrete rough paths. SIAM J. Math. Data Sci. 5 (2023), no. 1, pp. 50–76.
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Tropical time series, iterated-sums signatures and quasisymmetric functions. SIAM J. Appl. Algebra Geom. 6 (2022), no. 4, pp. 563–599.
- P. Hager, P. K. Friz, N. Tapia. Unified signature cumulants and generalized Magnus expansions. Forum Math. Sigma 10 (2022), no. e42.
- J. Diehl, R. Preiß, M. Ruddy, N. Tapia. The moving frame method for iterated-integrals: orthogonal invariants. Found. Comput. Math. (2022)
- K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti. Wick polynomials in non-commutative probability. Canad. J. Math. 74 (2021), no. 6, pp. 1673–1699.
- C. Bellingeri, A. Djurdjevac, P. K. Friz, N. Tapia. Transport and continuity equations with (very) rough noise. Partial Differ. Equ. Appl. 2 (2021), no. 49.
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Iterated-sums signature, quasisymmetric functions and time series analysis. Sém. Lothar. Combin. 84B (2020), Article 84B.86, 12 pp.
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Time-warping invariants of multidimensional time series. Acta Appl. Math. 171 (2020), no. 1, pp. 265–290.
- N. Tapia, L. Zambotti. The geometry of the space of branched Rough Paths. Proc. London Math. Soc. 121 (2020), no. 2, pp. 220–251.
- K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti. Hopf-algebraic deformations of products and Wick polynomials. Int. Math. Res. Not. 2020 (2020), no. 24, pp. 10064–10099.
- E. Celledoni, P.E. Lystad, N. Tapia. Signatures in Shape Analysis: an Efficient Approach to Motion Identification. (2019) In Geometric Science of Information. GSI 2019. Lect. Notes Comput. Sci. vol. 11712
- K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti. Shifted substitution in non-commutative multivariate power series with a view toward free probability. (2022) arXiv:2204.01445 [math.PR]
- M. Ghani Varzaneh, S. Riedel, A. Schmeding, N. Tapia. The geometry of controlled rough paths. (2022) arXiv:2203.05946 [math.PR]
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Generalized iterated-sums signatures. (2020) arXiv:2012.04597 [math.RA]
- Transport and continuity equations with (very) rough noise. Report for Oberwolfach Mini-Workshop 2207c "Regularization by noise: Theoretical foundations, numerical methods and applications". Oberwolfach Reports (2022). Published online: 2022-04-12
- Unified signature cumulants and generalized Magnus expansions. Report for Oberwolfach Workshop 2050a "New Directions in Rough Path Theory". Oberwolfach Reports 17 (2020), no. 4, pp. 1955–2019. Published online: 2021-09-13
- Guest editor for a special issue of "Symmetry, Integrability and Geometry: Methods and Applications" (SIGMA). Non-commutative Algebra, Probability and Analysis in Action.
- Non-commutative Algebra, Probability and Analysis in Action @ Greifswald, Germany. September 20—25, 2021.
- LMMS Summer School: Mathematical Methods for Machine Learning @ Dagstuhl, Germany. August 23—26, 2021.
- 10th World Congress in Probability and Statistics, Online. July 19—23, 2021.
- TMS Summer School for young researchers between geometry and stochastic analysis, Online. June 16--18, 2021. Website.
- Mini-workshop: SPDEs & friends.
- CIRM Meeting: Pathwise Stochastic Analysis and Applications. March 8—12, 2021.
- Mini-workshop: Cumulants in Stochastic Analysis.
- 14th Berlin-Oxford meeting. February 10—12, 2021.
- Rough paths and SPDEs, Online. December 9—11, 2020.
- MFO Meeting: New directions in Rough Paths theory, Online. December 7—11, 2020.
- Higher structures emerging from renormalisation, Online. October 12—16, 2020.
- Bernoulli-IMS One World Symposium, Online. August 24—28, 2020.
- Geometry of curves in time series and shape analysis, Online. August 11—14, 2020
- 13th Oxford-Berlin meeting, Online. June 8—10, 2020.
- Young researchers between geometry and stochastic analysis @ Bergen, Norway. February 12—14, 2020.
- 12th Oxford-Berlin meeting @ Alan Turing Institute Oxford, UK. December 4—6, 2019.
- Visit: INI Program @ Oxford, UK. December 1—12, 2019.
- Analytic and Algebraic perspectives in the theory of rough paths and signatures @ Oslo, Norway. November 14—15, 2019.
- Recontre GDR Renormalisation @ Calais, France. September 30—October 4, 2019.
- GSI'19: Geometric Science of Information @ Toulouse, France. August 27—29, 2019.
- Summer School: Mathematics of Deep Learning @ Berlin, Germany. August 19—30, 2019.
- SciCADE @ University of Innsbruck, Austria. July 22—26, 2019.
- 11th Oxford-Berlin meeting @ WIAS Berlin, Germany. May 23—25, 2019.
- Noncommutative Stochastic Analysis 2019 @ NTNU Trondheim, Norway. May 8—10, 2019.
- New Directions in Stochastic Analysis: Rough Paths, SPDEs and Related Topics @ Zuse Institute. Berlin, Germany. March 18—22, 2019.
- MAGiC 2019 @ Ilsetra, Lillehammer, Norway. February 25—March 1st, 2019.
- Rencontres du GDR Renormalisation @ Laboratoire Blaise Pascal. Clermont-Ferrand, France. November 12—16, 2018.
- 10th Oxford-Berlin meeting @ Oxford Mathematical Institue. Oxford, UK. November 29th & 30th, December 1st, 2018.
Scholarships and awards
- ERCIM Postdoctoral Fellowship. October 1, 2018 — May 31, 2019.
- CONICYT Doctorado Nacional 2013. March 2013 — September 2017.