Dr. Nikolas Tapia

  • Address: Mohrenstraße 39, 10117 Berlin, Germany.
  • Office: Hausvogteiplatz 11, room 0.02
  • Telephone: +49 30 20372-448.
  • e-mail: tapia (at) wias (dash) berlin (dot) de.
  • 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 part of the Stochastic Algorithms and Nonparametric Statistics research group at the Weierstraß Institute for Applied Analysis and Stochastics, and the Work Group on Stochastics and Financial Mathematics at the Technical University of Berlin.
I work as a Postdoctoral Researcher in the MATH+ EF1-13 project "Stochastic and rough aspects in deep neural networks", led by P. K. Friz and C. Bayer.
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.

Online Events:

Current Projects

Preprints and Publications

Articles in Refereed Journals

  1. J. Diehl, K. Ebrahimi-Fard, N. Tapia. Tropical time series, iterated-sums signatures and quasisymmetric functions. (2022) To appear in SIAM J. Appl. Algebra Geom. (SIAGA). arXiv:2009.08443 [math.RA]
  2. P. Hager, P. K. Friz, N. Tapia. Unified signature cumulants and generalized Magnus expansions. Forum Math. Sigma 10 (2022), no. e42.
  3. J. Diehl, R. Preiß, M. Ruddy, N. Tapia. The moving frame method for iterated-integrals: orthogonal invariants. Found. Comput. Math. (2022)
  4. K. Ebrahimi-Fard, F. Patras, N. Tapia, L. Zambotti. Wick polynomials in non-commutative probability. Canad. J. Math. (2021)
  5. 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.
  6. 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.
  7. J. Diehl, K. Ebrahimi-Fard, N. Tapia. Time-warping invariants of multidimensional time series. Acta Appl. Math. 171 (2020), no. 1, pp. 265–290.
  8. N. Tapia, L. Zambotti. The geometry of the space of branched Rough Paths. Proc. London Math. Soc. 121 (2020), no. 2, pp. 220–251.
  9. 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.
  10. 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. 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]
  2. M. Ghani Varzaneh, S. Riedel, A. Schmeding, N. Tapia. The geometry of controlled rough paths. (2022) arXiv:2203.05946 [math.PR]
  3. C. Bayer, P. K. Friz, N. Tapia. Stability of deep Neural Networks via discrete rough paths. (2022) WIAS Preprint no. 2732, arXiv:2201.07566 [cs.LG]
  4. J. Diehl, K. Ebrahimi-Fard, N. Tapia. Generalized iterated-sums signatures. (2020) arXiv:2012.04597 [math.RA]

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