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

Preprints

33. Karen Habermann, Philipp Harms, Stefan Sommer.
    Long-time existence of Brownian motion on configurations of two landmarks.
    arXiv:2304.14218.
34. Martin Bauer, Philipp Harms, Peter W. Michor.
    Regularity and completeness of half-Lie groups.
    arXiv:2302.01631.
35. Johannes Assefa, Philipp Harms.
    Cylindrical stochastic integration and applications to financial term structure modeling.
    arXiv:2208.03939.
36. Philipp Harms, Elodie Maignant, Stefan Schlager.
    Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifolds.
    arXiv:1904.11860.

Publications

1. Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer.
   Geometry of sample spaces.
   Differential Geometry and its Applications (forthcoming). arXiv:2010.08039.
2. Maren Hackenberg, Philipp Harms, Michelle Pfaffenlehner, Astrid Pechmann, Janbernd Kirschner, Thorsten Schmidt, Harald Binder.
   Deep dynamic modeling with just two time points: Can we still allow for individual trajectories?
   Biometrical Journal 64 (2022), pp. 1426-1445. arXiv:2012.00634.
3. 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 389, 899-931 (2022). arXiv:1810.03169.
4. 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.
5. 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.
6. 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.
7. 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.
8. Philipp Harms.
   Anmerkung zu OGH 23. 5. 2019 3 Obj 46/19i aus finanzmathematischer Sicht.
   Zeitschrift für Finanzmarktrecht 222 (2019), pp. 517-519.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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.
23. 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.
24. 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.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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
scholar.google.com/citations?user=Jv5PE9MAAAAJ
dr.ntu.edu.sg/cris/rp/rp01683

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University Singapore,
21 Nanyang Link #05-41, Singapore 637371

Last updated in May 2023 by Philipp Harms.