Professor Mallat is an applied mathematician, he is a member of the French Academy of Sciences and a foreign member of the US National Academy of Engineering. He was previously Professor at the Courant Institute of NYU, at Ecole Polytechnique and Ecole Normale Superieure in Paris. He also was a founder and CEO of a semiconductor start-up company. He developed the multiresolution wavelet theory and algorithms at the origin of the compression standard JPEG-2000, and sparse signal representations in dictionaries with matching pursuits. His current work is devoted to mathematical models of deep neural networks, for data analysis and physics.