Dr. Nikolas Tapia

  • Address: Anton-Wilhelm-Amo-Straße 39, 10117 Berlin, Germany.
  • Office: 208
  • Telephone: +49 30 20372-448.
  • e-mail: lastname (at) FQDN of this page.
  • Here is my PGP public key. Fingerprint: fe:8b:40:ee:4d:7f:15:b9:a0:67:63:9f:7f:db:7a:f5:18:50:35:fc
  • My CV.
    MR

I am member of the Stochastic Algorithms and Nonparametric Statistics group at WIAS. Currently, I work as a Postdoctoral Researcher in CRC/TRR 388, Project B01 led by Carlos Améndola, Christian Bayer and Markus Reiß. Previously, I was an associate researcher in MATH+ Excellence Cluster (projects EF1-5, EF1-13, AA4-2) and member of the Differential Equations and Numerical Analysis group at NTNU, working with K. Ebrahimi-Fard.
I hold a joint PhD in Mathematics from the University of Chile and Sorbonne Université, supervised by 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:

Preprints and Publications

Articles in Refereed Journals

  1. Branched Itô forumla and natural Itô-Stratonovich isomorphism, with C. Bellingeri, and E. Ferrucci. Adv. Math 484 (2026), 110687.
  2. On expected signatures and signature cumulants in semimartingale models, with P. K. Friz, and P. P. Hager. In Signature Methods in Finance, Bayer, C, dos Reis, G., Horvath, B., Oberhauser, H., eds. (2026)
  3. An introduction to tensors for path signatures, with J. Beda, and G. dos Reis. In Signature Methods in Finance, Bayer, C, dos Reis, G., Horvath, B., Oberhauser, H., eds. (2026)
  4. Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra, with L. Schmitz. Comm. Algebra (2025), pp. 1--25.
  5. The geometry of controlled rough paths, with M. Ghani Varzaneh, S. Riedel, and A. Schmeding. Stoch. Proc. Appl. 184 (2025), 1049594.
  6. Generalized iterated-sums signatures, with J. Diehl, and K. Ebrahimi-Fard. J. Algebra 623 (2023), pp. 801–824.
  7. Shifted substitution in non-commutative multivariate power series with a view toward free probability, with K. Ebrahimi-Fard, F. Patras, and L. Zambotti. SIGMA Symmetry Integrability Geom. Methods Appl. 19 (2023), 038, 17 pp.
  8. Stability of deep Neural Networks via discrete rough paths, with C. Bayer, and P. K. Friz. SIAM J. Math. Data Sci. 5 (2023), no. 1, pp. 50–76.
  9. Tropical time series, iterated-sums signatures and quasisymmetric functions, with J. Diehl, and K. Ebrahimi-Fard. SIAM J. Appl. Algebra Geom. 6 (2022), no. 4, pp. 563–599.
  10. Unified signature cumulants and generalized Magnus expansions, with P. Hager, and P. K. Friz. Forum Math. Sigma 10 (2022), no. e42.
  11. The moving frame method for iterated-integrals: orthogonal invariants, with J. Diehl, R. Preiß, and M. Ruddy. Found. Comput. Math. (2022).
  12. Wick polynomials in non-commutative probability, with K. Ebrahimi-Fard, F. Patras, and L. Zambotti. Canad. J. Math. 74 (2021), no. 6, pp. 1673–1699.
  13. Transport and continuity equations with (very) rough noise, with C. Bellingeri, A. Djurdjevac, and P. K. Friz. Partial Differ. Equ. Appl. 2 (2021), no. 49.
  14. Iterated-sums signature, quasisymmetric functions and time series analysis, with J. Diehl, and K. Ebrahimi-Fard. Sém. Lothar. Combin. 84B (2020), Article 84B.86, 12 pp.
  15. Time-warping invariants of multidimensional time series, with J. Diehl, and K. Ebrahimi-Fard. Acta Appl. Math. 171 (2020), no. 1, pp. 265–290.
  16. The geometry of the space of branched Rough Paths, with L. Zambotti. Proc. London Math. Soc. 121 (2020), no. 2, pp. 220–251.
  17. Hopf-algebraic deformations of products and Wick polynomials, with K. Ebrahimi-Fard, F. Patras, and L. Zambotti. Int. Math. Res. Not. 2020 (2020), no. 24, pp. 10064–10099.
  18. Signatures in Shape Analysis: an Efficient Approach to Motion Identification, with E. Celledoni, and P.E. Lystad. In Geometric Science of Information. GSI 2019. Lect. Notes Comput. Sci. vol. 11712 (2019).

Preprints

  1. Explicit and Effectively Symmetric Runge-Kutta Methods, with D. Shmelev, K. Ebrahimi-Fard and C. Salvi. (2025) arXiv:2507.21006 [math.NA]
  2. Perturbative renormalisation of the (Φ4)4-ε model via generalized Wick maps, with N. Berglund and T. Klose. (2025) arXiv:2507.03820 [math.PR]
  3. A multiplicative surface signature through its Magnus expansion, with I. Chevyrev, J. Diehl, and K. Ebrahimi-Fard. (2024) arXiv:2406.16856 [math.RA]

Other publications

  1. Branched Itô formula and natural Itô-Stratonovich isomorphism. Report for Oberwolfach Mini-Workshop 2445 "Directions in Rough Analysis". Oberwolfach Reports 21 (2022), no. 4, pp. 2927–2928. Published online: 2025-05-19
  2. 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 19 (2022), no. 1, pp. 457–488. Published online: 2022-04-12
  3. 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). Asymptotics, Randomness and Noncommutativity.
  2. 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