Department of Mathematics

Matthew John Hirn

Picture of Matthew John Hirn

Assistant Professor (joint with CMSE)

  • Ph.D., University of Maryland, 2009


Office Hours
  • 3:00 PM - 4:00 PM
  • 3:00 PM - 4:00 PM
Research Interests

My research is in pure, applied, and computational harmonic analysis, motivated in large part by a desire to rigorously understand the mathematical underpinnings of machine learning algorithms. This understanding in turn leads to the development of new machine learning paradigms, particularly for the analysis of high dimensional data. Finally, these methods are leveraged to open up new avenues for scientific breakthroughs, either by circumventing prohibitively costly computations or by revealing unforeseen patterns in complex data. 

My primary interests range over pure and applied topics, but can be loosely summarized as:

- Wavelet theory, particularly how it relates to deep learning (scattering transforms)
- Diffusion based manifold learning
- Smooth extensions and interpolations of Whitney type
- Quantum chemistry and many body problems
- Applications in bio-medical data analysis

Selected Publications
  • Wavelet Scattering Regression of Quantum Chemical Energies. With Stéphane Mallat and Nicolas Poilvert. Multiscale Modeling and Simulation, to appear, 2017. arXiv:1605.04654.  Open
  • Computing minimal interpolants in C^{1,1}(R^d). With Ariel Herbert-Voss and Frederick McCollum. Revista Matemática Iberoamericana, volume 33, issue 1, pages 29-66, 2017. arXiv:1411.5668.  Open
  • A general theorem of existence of quasi absolutely minimal Lipschitz extensions. With Erwan Le Gruyer. Mathematische Annalen, volume 359, issue 3-4, pages 595-628, August 2014.  Open
  • Diffusion maps for changing data. With Ronald R. Coifman. Applied and Computational Harmonic Analysis, volume 36, issue 1, pages 79-107, January 2014.  Open
  • Bi-stochastic kernels via asymmetric affinity functions. With Ronald R. Coifman. Applied and Computational Harmonic Analysis, volume 35, issue 1, pages 177-180, July 2013.  Open
  • Wavelet packets for multi- and hyper-spectral imagery. With John J. Benedetto, Wojciech Czaja, Martin Ehler and Justin C. Flake. In Proceedings of IS&T/SPIE Electronic Imaging 2010, Wavelet Applications and Industrial Processing VII, volume 7535, San Jose, California, January 2010.  Open
  • Frame based kernel methods for automatic classification in hyperspectral data. With John J. Benedetto, Wojciech Czaja and Justin C. Flake. In Proceedings of the IEEE 2009 International Geoscience and Remote Sensing Symposium, volume 4, pages 697-700, Cape Town, South Africa, July 12-17, 2009.  Open