# 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:
`fe:8b:40:ee:4d:7f:15:b9:a0:67:63:9f:7f:db:7a:f5:18:50:35:fc`

- 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).

## 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

- K. Ebrahimi-Fard, F. Patras, N. Tapia. L. Zambotti.
*Wick polynomials in non-commutative probability*. Canad. J. Math. (2021) - 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. Lecture Notes in Computer Science vol. 11712*

### 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]

### Other publications

*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

- 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

- 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.