Ron DeVore (Dep. of Mathematics,Texas A&M University, USA, recipient of the Foundation's Research Chaire of Excellence 2009) and Albert Cohen (UPMC, LJLL) organized a two days workshop about Dimensional Problems and Solutions on June 21th and 22th 2010 in the UPMC.
Several important areas of science are confronted with the having to recover a functions of many variables either from large data sets or from complex mathematical models. Such recovery is inhibited by what is commonly called the 'curse of dimensionality' which says the numerical approximation of such a function will require inordinately more computation as the number of active variables increases. This workshop bring together the world's leading experts on high dimensional problems to discuss their recent research in areas such as manifold learning, stochastic and parametric PDEs, and optimal recovery.
- Steve Smale (Université CityU de Hong Kong) "Hodge Theory"
- Mauro Maggioni (Duke) "Multiscale geometric methods for the analysis of points clouds"
- Gilad Lerman (Univ. du Minnesota) "Multi-Manifold Data Modeling: Foundations and Applications"
- Christoph Schwab (ETH Zurich) "Sparse Tensor Approximations of PDEs on high-dimensional parameter spaces" (click here to download the presentation)
-Yvon Maday (Paris VI) "Reduced basis and magic point for high dimensional approximation problems"
- Wolfgang Dahmen (RWTH Aachen) "A greedy approach for the reduced basis method - Convergence rates" (click here to download the presentation)
- Emmanuel Vazquez (Supelec) "Gaussian processes, RKHS and their applications to computer experiments" (click on the first, the second, the third, the fourth and the fifth part of the presentation to download them)
- Peter Binev (Univ. Caroline du Sud) "Sparse Occupancy Trees" (click here to download the presentation)
- Przemek Wojtaszczyk (Univ. de Varsovie) "Approximation of functions of few variables in high dimension " (click here to download the presentation)
- Dominique Picard (Paris VII) "LOL: thresholdings and high dimensions" (click here to download the presentation)
- Rob Nowak (Univ. du Wisconsin) "Adaptive and Nonlinear Designs for Large-Scale Multiple Hypothesis Testing"
- Martin Wainwright (Berkeley) "Recovery problems in high dimensions: A unified analysis of estimators with decomposable regularizers"
- Stephane Mallat (Polytechnique) "High dimensional classification by recursive interferometry"