Dr. Nikolas E. Tapia M.
- 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:
FE8B 40EE 4D7F 15B9 A067 639F 7FDB 7AF5 1850 35FC
- 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+ 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.
Online Events:
- I co-organize the Algebraic and Combinatorial Perspectives in the Mathematical Sciences seminar (Fridays @ 15:00 CET).
- Mini-workshop: Cumulants in Stochastic Analysis.
- Mini-workshop: SPDEs & friends.
- TMS Summer School for young researchers between geometry and stochastic analysis. June 15--19, 2021 @ UiA, Kristiansand, Norway. Website.
Live events:
- Workshop: "Noncommutative algebra, probability and analysis in action". September 20--25, 2021 @ U. Greifswald, Greifswald, Germany. Website.
Current Projects
- Robustness of Deep Neural Networks, with Christian Bayer and Peter Friz.
- Discrete-time signatures, with Joscha Diehl and Kurusch Ebrahimi-Fard.
- Geometric aspects of rough paths, with Mazyar Ghani, Sebastian Riedel, and Alexander Schmeding.
- Numerical methods for linear rough SPDEs, with Ana Djurdjevac and Christian Bayer.
Preprints and Publications
Articles in Refereed Journals
- C. Bellingeri, A. Djurdjevac, P. K. Friz, N. Tapia. Transport and continuity equations with (very) rough noise. To appear in Partial Differ. Equ. Appl. PDEA (2021). arXiv:2002.10432 [math.AP]
- 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.
- 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. Lecture Notes in Computer Science vol. 11712
- 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.
Preprints
- P. Hager, P. K. Friz, N. Tapia. Unified signature cumulants and generalized Magnus expansions. (2021) arXiv:2102.03345 [math.PR]
- J. Diehl, R. Preiß, M. Ruddy, N. Tapia. The moving frame method for iterated-integrals: orthogonal invariants. (2020) arXiv:2012.05880 [math.DG]
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Generalized iterated-sums signatures. (2020) arXiv:2012.04597 [math.RA]
- C. Bayer, P. K. Friz, N. Tapia. Stability of deep Neural Networks via discrete rough paths. (2020) WIAS Preprint no. 2732
- J. Diehl, K. Ebrahimi-Fard, N. Tapia. Tropical time series, iterated-sums signatures and quasisymmetric functions. (2020) arXiv:2009.08443 [math.RA]
- K. Ebrahimi-Fard, F. Patras, N. Tapia. L. Zambotti. Wick polynomials in non-commutative probability. (2020) arXiv:2001.03808 [math.PR]
Talks
- Free Wick polynomials. Potsdam Analysis Seminar. Online. Slides
- Higher-order iterated sums signatures. Seminar: DataSig. Online. Slides
- Strong solutions for the rough transport equation with any Hölder regularity. Seminar: Research group FOR2402. TU Berlin, Germany.
- Non-commutative Wick polynomials. Rencontre GDR Renormalisation. Calais, France. Slides
- Signatures in Shape Analysis. GSI'19. Toulouse, France. Slides
- Algebraic aspects of signatures. SciCADE 2019. Innsbruck, Austria. Slides
- Signatures in Shape Analysis. 11th Oxford-Berlin meeting. Berlin, Germany. Slides
- Noncommutative Wick polynomials. Noncommutative Stochastic Analysis 2019. Trondheim, Norway. Slides
- The signature method. Nucleo Milenio Modelos Estocasticos de Sistemas Complejos y Desordenados. Santiago, Chile. Slides
- An introduction to signatures. MAGiC 2019. Ilsetra, Lillehammer, Norway. Slides
- Modification of Branched Rough Paths. NTNU Trondheim. Slides
- The geometry of the space of branched Rough Paths. Max-Planck-Institute. Leipzig, Germany. Slides
- The geometry of the space of branched Rough Paths. Rencontres du GDR Renormalisation. Clermont-Ferrand, France. Slides
Upcoming Events
- 14th Berlin-Oxford meeting. February 10—12, 2021.
- CIRM Meeting: Pathwise Stochastic Analysis and Applications. March 8—12, 2021.
Past Events
- 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.