Turing Lecture: Mathematics

Speaker 1: Stéphane Mallat, Ecole Normale Superieure

High-Dimensional Learning and Deep Neural Networks

Classifications and regressions from data requires to approximate functions in high dimensional spaces. Avoiding the curse of dimensionality raises issues in many branches of mathematics including statistics, probability, harmonic analysis and geometry. Recently, deep convolutional networks have obtained spectacular results for image understanding, audio recognition, natural language analysis and all kind of data analysis problems. We shall review their architecture, and analyze their mathematical properties, with many open questions. These architectures implement non-linear multiscale contractions, and sparse separations, where wavelets play an important role. Applications are shown for image and audio classification, as well as quantum energy regressions.

Biography

Stéphane Mallat received a Ph.D. from the University of Pennsylvania, in 1988. He was then Professor at the Courant Institute of Mathematical Sciences, until 1994. In 1995, he became Professor in Applied Mathematics at Ecole Polytechnique, Paris and Department Chair in 2001. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. In 2012 he joined the Computer Science Department of Ecole Normale Supérieure, in Paris. Stéphane Mallat is a member of the French Academy of sciences. His research interests include learning, signal processing, and harmonic analysis. He is an IEEE Fellow and an EUSIPCO Fellow. In 1997, he received the Outstanding Achievement Award from the SPIE Society and was a plenary lecturer at the International Congress of Mathematicians in 1998. He also received the 2004 European IST Grand prize, the 2004 INIST-CNRS prize for most cited French researcher in engineering and computer science, the 2007 EADS grand prize of the French Academy of Sciences, the 2013 Innovation medal of the CNRS, and the 2015 IEEE Signal Processing best sustaining paper award.

Speaker 2: Mark Newman, University of Michigan

Epidemics, Erdos numbers, and the Internet: The Form and Function of Networks

There are networks in almost every part of our lives: the Internet, the power grid, road and rail networks, networks of friendship or acquaintance, ecological networks, biochemical networks, and many others. As large-scale data on these networks have become available in the last few years, a new science of networks has grown up combining observations and theory to shed light on systems ranging from bacteria to the whole of human society. This talk will give an overview of some of the most important discoveries in this growing field, how those discoveries were made, and what they can tell us about the way the world works.

Biography

Mark Newman received a DPhil in theoretical physics from Oxford University in 1991 and conducted postdoctoral research at Cornell University before taking a position at the Santa Fe Institute, a think-tank in New Mexico known for its work on the theory of complex systems. He left Santa Fe in 2002 for the University of Michigan where he is currently the Anatol Rapoport Distinguished University Professor of Physics and a professor in the university's Center for the Study of Complex Systems. Among other honors, Professor Newman is a Fellow of the American Physical Society, a Fellow of the American Association for the Advancement of Science, and was the winner of the 2014 Lagrange Prize, the largest international prize for research in complex systems. His research is in statistical physics and combines traditional ideas such as percolation theory, disordered systems, and Monte Carlo methods with nontraditional applications, particularly to networked systems such as social and computer networks. He is the author of over 150 scientific publications and seven books, including "Networks", an introduction to the field of network theory, and "The Atlas of the Real World", a popular book on cartography.