Research

I use geometric and topological tools both within pure Math and in Computer Science. My main area of research is Machine Learning (statistical machine learning, topological data analysis) but I also work on certain problems in Contact/Symplectic Geometry as well as Computational Geometry. My focus in Machine Learning is its interaction with Neuroscience  understanding theoretical principles governing both artificial and biological learning, developing dataanalytic tools for neuroscience data, and taking inspiration from biological learning to develop machine learning algorithms.
Google Scholar entry.
Recent publications and preprints
N. Denis, M. Fraser, Options and partial observability: regret bounds by analogy with semisupervised learning. NIPS2018 Reinforcement Learning Under Partial Observability Workshop, December 2018.
M. Fraser, L. Polterovich, D. Rosen, On Sandontype metrics for contactomorphism groups. Ann. Math. Québec, 2018. onlinedoi. (arxiv version)
N. Denis, M. Fraser, Landmark Options Via Reflection (LOVR) in MultiTask Lifelong Reinforcement Learning. NIPS2017 Hierarchical Reinforcement Learning Workshop (oral presentation and poster; nonproceedings pdf), December 2017.
M. Fraser, Contact nonsqueezing at large scale in ℝ^{2n} x S^{1}. International Journal of Mathematics, (27)13, pp. 6085, 2017. (arxiv version)
M. Fraser, Multistep learning and underlying structure in statistical models. NIPS2016. (proceedings pdf)
M. Fraser, Contact nonsqueezing via generating functions: A lowtech proof in the language of persistence modules. Poster in Summer School 2016 on Symplectic Topology, Sheaves and Mirror Symmetry, Paris IJMPRG, 2016. (poster)
M. Fraser, Contact spectral invariants and persistence, preprint 2015. (arxiv version)
M. Fraser, Group Actions in Topological Data Analysis and Hierarchical Learning. PhD Thesis, Dept. of Computer Science, University of Chicago, August 2013.
M. Fraser, Tight Linear Lower Memory Bound for Local Routing in Planar Digraphs. In Proceedings of Canadian Conference on Computational Geometry (CCCG12), August 2012. (proceedings pdf)
M. Fraser, Persistent Homology of filtered covers. 2012. (arxiv version)
M. Fraser, Local Routing in Graphs Embedded on Surfaces of Arbitrary Genus. 2012. (arxiv version)
M. Fraser, Structural Observations on Neural Networks for Hierarchically Derived Reproducing Kernels. University of Chicago Master's thesis, November 2011. (revised version) (slides)
 M. Fraser, Two Extensions to Manifold Learning Algorithms Using αComplexes. Dept. of Computer Science, University of Chicago, Technical Report TR201007, 2010.
A. Fraser, D. Fraser, M. Fraser, Curvature Revisited and the BayesFrequentist Divergence. In Journal of Statistical Research, Vol 44 number 2, 2010. (pdf)
Y. Eliashberg and M. Fraser, Topologically Trivial Legendrian Knots. In Journal of Symplectic Geometry, Vol. 7, pp.77127, 2009. (arxiv version)
E. Chávez, M. Fraser and H. Tejeda, Proximal Labeling for Oblivious Routing in Wireless Ad Hoc Networks. In Proceedings of ADHOCNOW 2009, Springer Verlag LNCS 5793, pp. 360365.
M. Fraser, E. Kranakis, J. Urrutia, Memory Requirements for Local Geometric Routing or Traversal in Digraphs. In Proceedings of Canadian Conference on Computational Geometry (CCCG08), August 2008. (proceedings pdf)
M. Fraser, Local Routing on Tori (extended, invited version of next paper). In Ad Hoc and Sensor Wireless Networks, journal issue dedicated to ADHOCNOW 2007, Vol. 6, pp. 179196, 2008.
M. Fraser, Local Routing on Tori. In proceedings of ADHOCNOW 2007, Springer Verlag LNCS 4686, pp. 153166, E. Kranakis and J. Opatrny (Eds.), Morelia, September 2007.
Teaching
 MAT4376B/5314: Statistical Machine Learning
 MAT1741: Algèbre linéaire
 MAT3153: Introduction to Topology (using this textbook)
Previously at University of Toronto:
TA'ing at University of Chicago:
 CMSC28100 Introduction to Complexity Theory
 CMSC25010 Introduction to AI
 CMSC15300 Foundations of Software