Dr. Nikolas Tapia

  • Address: Mohrenstraße 39, 10117 Berlin, Germany.
  • Office: 208
  • Telephone: +49 30 20372-448.
  • e-mail: lastname (at) FQDN of this page.
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  • My CV.
    MR

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 CRC/TRR 388 "Rough Analysis, Stochastic Dynamics and Related Fields", Project B01 "Statistical learning from path observations" led by Carlos Améndola, Christian Bayer and Markus Reiß. I am a former member of the MATH+ Excellence Cluster as associate researcher for projects EF1-5, EF1-13 and AA4-2. Previously, I was a member 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.

Portrait of Nikolas Tapia, a postdoctoral researcher at the Weierstrass Institute. He is standing in front of a traditional Japanese building, wearing glasses and a white shirt, and smiling at the camera.

📷 Geraldine Cossio, 2023.

Online Events:

Current Projects

Preprints and Publications

Articles in Refereed Journals

  1. J. Diehl, K. Ebrahimi-Fard, N. Tapia. Generalized iterated-sums signatures. J. Algebra 623 (2023), pp. 801–824.
  2. K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti. Shifted substitution in non-commutative multivariate power series with a view toward free probability. SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), 038, 17 pp.
  3. 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.
  4. 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.
  5. P. Hager, P. K. Friz, N. Tapia. Unified signature cumulants and generalized Magnus expansions. Forum Math. Sigma 10 (2022), no. e42.
  6. J. Diehl, R. Preiß, M. Ruddy, N. Tapia. The moving frame method for iterated-integrals: orthogonal invariants. Found. Comput. Math. (2022).
  7. 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.
  8. 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.
  9. 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.
  10. J. Diehl, K. Ebrahimi-Fard, N. Tapia. Time-warping invariants of multidimensional time series. Acta Appl. Math. 171 (2020), no. 1, pp. 265–290.
  11. N. Tapia, L. Zambotti. The geometry of the space of branched Rough Paths. Proc. London Math. Soc. 121 (2020), no. 2, pp. 220–251.
  12. 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.
  13. 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

Preprints

  1. P. K. Friz, P. P. Hager, N. Tapia. On expected signatures and signature cumulants in semimartingale models. (2024) arXiv:2408.05085 [math.PR]
  2. I. Chevyrev, J. Diehl, K. Ebrahimi-Fard, N. Tapia. A multiplicative surface signature through its Magnus expansion. (2024) arXiv:2406.16856 [math.RA]
  3. L. Schmitz, N. Tapia. Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra. (2024) arXiv:2401.06691 [math.RA]
  4. C. Bellingeri, E. Ferrucci, N. Tapia. Branched Itô forumla and natural Itô-Stratonovich isomorphism. (2023) arXiv:2312.04523 [math.PR]
  5. M. Ghani Varzaneh, S. Riedel, A. Schmeding, N. Tapia. The geometry of controlled rough paths. (2022) arXiv:2203.05946 [math.PR]

Other publications

  1. 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
  2. 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

Editorial Work

  1. Guest editor for a special issue of "Symmetry, Integrability and Geometry: Methods and Applications" (SIGMA). Non-commutative Algebra, Probability and Analysis in Action.

Upcoming Events

Past Events

Scholarships and awards