My interests are in harmonic analysis, wavelets, multiscale analysis in general, and in particular with applications to the analysis of graphs and data sets viewed as discrete or sampled continuous geometric structures embedded in high-dimensional spaces. I am interested in machine learning problems, mostly from the point of view of approximation and fitting of functions under random noise and random sampling.

  1. Diffusion Wavelets: a recent construction of new families of wavelets and Multi-resolution Analyses on graphs, manifolds and point clouds. Pictures, papers and presentations available.
  2. Diffusion Geometries: here are some links to the use of diffusion geometries in data analysis.
  3. Analysis of Molecular Dynamics Data: in collaboration with Cecilia Clementi, Mary Rohrdanz and Wenwei Zheng, we use the geometric structure of data generated from molecular dynamics data to construct observables that provide reaction coordinates and reduced, low-dimensional dynamics that well-approximates the long-time dynamics of the original system.
  4. Multiscale Analysis of Markov Decision Processes
  5. Visualization of large data sets.
  6. Harmonic Analysis and Wavelets: here I talk a bit about Harmonic Analysis and provide links to related web pages.
  7. HyperSpectral Imaging and Pathology: hyper-spectral imaging applied to pathology

Postdocs and students

OPEN POSITIONS! My lab has open positions for graduate students and postdocs. See the ads on mathjobs.

Current & past: Jake Bouvrie, Guangliang Chen, Miles Crosskey (now at CoVar Applied Technologies), Mark Iwen, David Lawlor, Stas Minsker, Jason Lee, Nate Strawn (currently at Georgetown University), Josh Vogelstein

Past: Yoon-Mo Jung, Prakash Balachandran, Anna V Little.

Pointers to some future, present and recent past happenings

NEW!! Duke Workshop on Sensing and Analysis of High-Dimensional Data, July 23-25, 2013

Structure in Complex Data Set Duke Mathematics N.S.F.-funded Research Training Grant.

Triangle Computer Science Distinguished Lecturer Series

Mathematical Biology Duke Mathematics N.S.F.-funded Research Training Grant.

Computational Geometry Week, including ACM SoCG 2012, June 17-20, in Chapel Hill, NC, USA. Special workshop Connections between analysis and computational geometry, organized by Chris Bishop. See also the special workshop Computational Geometric Learning Exploring geometric structure in high dimensions organized by J. Giesen, C.K. Müller, G. Rote.

Challenges in Geometry, Analysis and Computation: High_Dimensional Synthesis June 4-6 2012. A conference in honor of R.R. Coifman, P.W. Jones and V. Rokhlin.

I.M.A. Thematic Year on the Mathematics of Information 2011-12

ICIAM Minisymposium on Harmonic Analysis on Graphs and Networks on July 22, 2011

Duke workshop on Sensing and Analysis of High-Dimensional Data on July 26-28th

AMS Special Session on The Mathematics of Information and Knowledge: a page with links and some of the slides of the talks here.

CTMS Workshop on Large Data Sets: Computation and Structure, Nov. 13th, Duke University, NC. The schedule will be available here.

Forum on Geometric Aspects of Machine Learning and Visual Analytics, Oct 11-12, IEEE VisWeek, Atlantic City, NJ.

SAMSI opening workshop on stochastic dynamics, part of the long program on stochastic dynamics.

Our Probability Wiki and working group at Duke. As of Spring 09, we are meeting every Tuesday at 1pm in Room 259 in the Physics building, to discuss topics of interest to the audience. It is informal, highly interdisciplinary, and fun. Papers/talks are collected on the wiki. Feel free to join us (or the mailing list).

Symposium on Manifold Learning to be held on Nov. 5-7 in Arlington, VA.

Compressive Sensing Workshop at Duke (slides and video lectures available).

Links of Interest

Programming, Code, etc...

Data Sets

The material presented at this web site is partially based upon work supported by the Alfred P. Sloan Foundation and the National Science Foundation. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author and do not necessarily reflect the views of the granting agencies.