Philipp Harms

Bio

I am an Associate Professor in mathematics at NTU Singapore since January 2022. Before, I was a Junior Professor at the University of Freiburg, a PostDoc at ETH Zürich and Harvard University, and a PhD student at the University of Vienna.

Research interests

Geometric data science. More specifically:

• Theory: differential geometry and stochastic analysis in infinite dimensions
• Applications: mathematics of deep learning, shape analysis, and mathematical finance

Open positions

Expressions of interest are invited for 3 doctoral and 3 postdoctoral positions at the Department of Mathematics, Nanyang Technological University (NTU) Singapore. The positions are part of the project Geometry, Probability, and Deep Learning funded by Singapore's National Research Foundation.

• The ideal candidates will have an excellent research background in at least one of these fields, including particularly in infinite-dimensional Riemannian or metric geometry, infinite-dimensional probability or stochastic analysis, statistical learning theory, coding theory, inverse problems, or harmonic analysis.
• The goal of this project is to use geometric and probabilistic methods for analyzing the effectiveness of deep learning, to use deep learning methods for improving algorithms in probability and geometry, to advance the mathematical foundations of these methods, and to develop applications in e.g. mathematical finance or biomedical shape analysis.
• The postdoctoral positions are for 2 years with optional prolongation to 3 years, and the doctoral positions for 2-5 years. All positions come with an attractive salary package. The expected starting date is mid 2022.

If you are interested, please send your CV, list of publications, and research statement (1-2 pages) to philipp.harms@ntu.edu.sg as soon as possible. The search will continue until the positions are filled.

Preprints

30. Maren Hackenberg, Philipp Harms, Thorsten Schmidt, Harald Binder.
    Deep dynamic modeling with just two time points: Can we still allow for individual trajectories?.
    arXiv:2012.00634.
31. Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer.
    Geometry of sample spaces.
    arXiv:2010.08039.
32. Philipp Harms, Elodie Maignant, Stefan Schlager.
    Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifolds.
    arXiv:1904.11860.

Publications

1. Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor.
   Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics.
   Communications in Mathematical Physics (2022). arXiv:1810.03169.
2. Martin Bauer, Nicolas Charon, Philipp Harms, Hsi-Wei Hsieh.
   A numerical framework for elastic surface matching, comparison, and interpolation.
   International Journal of Computer Vision 129 (2021), pp. 2425–2444. arXiv:2006.11652. Code available on github.com/SRNFmatch.
3. Philipp Harms, Chong Liu, Ariel Neufeld.
   Supermartingale deflators in the absence of a numéraire.
   Mathematics and Financial Economics 15, 885-915 (2021). arXiv:2001.05906.
4. Philipp Harms.
   Strong convergence rates for Markovian representations of fractional Brownian motion.
   Discrete and Continuous Dynamical Systems B 26, 10 (2021), pp. 5567-5579. arXiv:1902.01471.
5. Martin Bauer, Philipp Harms, Peter W. Michor.
   Fractional Sobolev metrics on spaces of immersions.
   Calculus of Variations and Partial Differential Equations 59, 62 (2020). arXiv:1909.08657.
6. Philipp Harms.
   Anmerkung zu OGH 23. 5. 2019 3 Obj 46/19i aus finanzmathematischer Sicht.
   Zeitschrift für Finanzmarktrecht 222 (2019), pp. 517-519.
7. Martin Bauer, Philipp Harms, Stephen C. Preston.
   Vanishing distance phenomena and the geometric approach to SQG.
   Archive for Rational Mechanics and Analysis 235 (2020), pp. 1445-1466. arXiv:1805.04401.
8. Martin Bauer, Nicolas Charon, Philipp Harms.
   Inexact elastic shape matching in the square root normal field framework.
   In: Geometric Science of Information. Springer (2019). arXiv:1903.00855.
9. Philipp Harms, Marvin Müller.
   Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schroedinger and linearized stochastic Korteweg-de Vries equations.
   Zeitschrift für Angewandte Mathematik und Physik 70, 16 (2019) . arXiv:1710.01273.
10. Philipp Harms, David Stefanovits.
    Affine representations of fractional processes with applications in mathematical finance.
    Stochastic Processes and their Applications 129, 4 (2019), pp. 1185-1228. arXiv:1510.04061.
11. Roland Fryer, Philipp Harms, Matthew Jackson.
    Updating Beliefs When Evidence is Open to Interpretation: Implications for Bias and Polarization.
    Journal of the European Economic Association 17, 5 (2019), pp. 1470-1501. SSRN 2263504.
12. Martin Bauer, Martins Bruveris, Philipp Harms, Peter Michor.
    Soliton solutions for the elastic metric on spaces of curves.
    Discrete and Continuous Dynamical Systems A 38, 3 (2018), pp. 1161-1185. arXiv:1702.04344.
13. Philipp Harms, David Stefanovits, Josef Teichmann, Mario Wüthrich.
    Consistent recalibration of yield curve models.
    Math. Fin. 28, 3 (2018), pp. 757-799. arXiv:1502.02926.
14. Roland Fryer, Philipp Harms.
    Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability.
    Math. Oper. Res. 43, 2 (2018), pp. 399-427. arXiv:1506.07291.
15. Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen.
    A numerical framework for Sobolev metrics on the space of curves.
    SIAM J. Imaging Sci. 10, 1 (2017), pp. 47-73. arXiv:1603.03480. Code available on https://github.com/h2metrics/h2metrics.
16. Philipp Harms, David Stefanovits, Josef Teichmann, Mario Wüthrich.
    Consistent recalibration of the discrete-time multifactor Vasicek model.
    Risks 4, 3 (2016), pp. 1-31. arXiv:1512.06454.
17. Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen.
    Second order elastic metrics on the shape space of curves.
    1st International Workshop on Differential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories, 2015. arXiv:1507.08816.
18. Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen.
    Curve Matching with Applications in Medical Imaging.
    5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 2015. arXiv:1506.08840.
19. Martin Bauer, Philipp Harms.
    Metrics on Spaces of Surfaces where Horizontality equals Normality.
    Differential Geometry and its Applications 39 (2015), pp. 166-183. arXiv:1403.1436.
20. Martin Bauer, Philipp Harms, Peter W. Michor.
    Sobolev Metrics on Shape Space, II: Weighted Sobolev Metrics and Almost Local Metrics.
    Journal of Geometric Mechanics 4, 4 (2012), pp. 365-383. arXiv:1109.0404.
21. Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor.
    Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group.
    Annals of Global Analysis and Geometry 44, 1 (2013), pp. 5-21. arXiv:1105.0327.
22. Martin Bauer, Philipp Harms, Peter W. Michor.
    Sobolev metrics on the manifold of all Riemannian metrics.
    Journal of Differential Geometry 94, 2 (2013), pp. 187-208. arXiv:1102.3347.
23. Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor.
    Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation.
    Annals of Global Analysis and Geometry 41, 4 (2012), pp. 461-472. arXiv:1102.0236.
24. Martin Bauer, Philipp Harms, Peter W. Michor.
    Curvature weighted metrics on shape space of hypersurfaces in n-space.
    Differential Geometry and its Applications 30, 1 (2012), pp. 33-41. arXiv:1102.0678.
25. Martin Bauer, Philipp Harms, Peter W. Michor.
    Sobolev metrics on shape space of surfaces.
    Journal of Geometric Mechanics 3, 4 (2011), pp. 389-438. arXiv:1009.3616.
    Erratum. A gap in Section 6.6 was discovered and corrected by Olaf Müller in his paper "Applying the index theorem to non-smooth operators." Journal of Geometry and Physics 116 (2017): 140-145.
26. Philipp Harms, Andrea C. G. Mennucci.
    Geodesics in infinite dimensional Stiefel and Grassmann manifolds.
    Comptes Rendus Mathematique 350, 15-16 (2012), pp. 773-776. arXiv:1209.2878.
27. Martin Bauer, Philipp Harms, Peter W. Michor.
    Almost local metrics on shape space of hypersurfaces in n-space.
    SIAM Journal on Imaging Sciences 5, 1 (2012), pp. 244-310. arXiv:1001.0717.

Technical reports

1. Philipp Harms, Elodie Maignant.
   Approximations of distances and kernels on shape space.
   Math in the Black Forest – Workshop on New Directions in Shape Analysis (2018). arXiv:1811.01370.
2. Martin Bauer, Philipp Harms.
   Hörmander's condition for normal bundles on spaces of immersions.
   Math on the Rocks – Shape Analysis Workshop in Grundsund (2015). arXiv:1511.05883.
3. Martin Bauer, Philipp Harms.
   Metrics with prescribed horizontal bundle on spaces of curves.
   Math on the Rocks – Shape Analysis Workshop in Grundsund (2015). arXiv:1511.05889.
4. Philipp Harms.
   Metrics on spaces of immersions where horizontality equals normality.
   Math in the Cabin – Shape Analysis Workshop in Bad Gastein (2014). eprint:hal‑01076953.

Theses

1. Sobolev metrics on shape space of surfaces.
   PhD thesis, University of Vienna, 2010. arXiv:1211.3515.
2. The Poincaré Lemma in Subriemannian Geometry.
   Master thesis, Vienna University of Technology, 2008. arXiv:1211.3531.

Code

1. Martin Bauer, Nicolas Charon, Philipp Harms, Hsi-Wei Hsieh.
   A numerical framework for elastic surface matching, comparison, and interpolation. github.com/SRNFmatch.
2. Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen.
   Tools for Riemannian shape analysis with second order Sobolev metrics. github.com/h2metrics.

Contact and Impressum

philipp.harms@ntu.edu.sg
Academic Profile at NTU
Last updated in January 2022 by Philipp Harms.