The fundamental aim of this program is to bring together a core group of mathematicians from the general communities of nonlinear dispersive and stochastic partial differential equations whose research contains an underlying and unifying problem: quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems, and in various regimes.
In recent years there has been spectacular progress within both communities in the understanding of this common problem. The main efforts exercised, so far mostly in parallel, have generated an incredible number of deep results, that are not just beautiful mathematically, but are also important to understand the complex natural phenomena around us. Yet, many open questions and challenges remain ahead of us. Hosting the proposed program at MSRI would be the most effective venue to explore the specific questions at the core of the unifying theme and to have a focused and open exchange of ideas, connections and mathematical tools leading to potential new paradigms. This special program will undoubtedly produce new and fundamental results in both areas, and possibly be the start of a new generation of researchers comfortable on both languages.Updated on Sep 15, 2015 05:25 PM PDT
Updated on Jan 26, 2015 04:20 PM PST
The theme of this workshop is on bringing theory into the study of neural networks---those in brains and those in machines. We will soon have the capability to monitor activity and structure in the brain at unprecedented scales, but what will these data tell us? It is unlikely that we will gain insight without some theoretical framework to guide our thinking of what to look for, and why. Similarly, neural network models can now perform feats of language translation and pattern recognition far beyond what was possible a few years ago; but they have yet to shed new light on neurobiological mechanisms in part because there is only a limited theory of such computations.
What are likely candidates for such theories? Do they already exist? And what is needed to more tightly integrate theoretical frameworks with empirical approaches?
Updated on Oct 05, 2015 03:32 PM PDT
Updated on Oct 05, 2015 01:29 PM PDT
Created on Sep 25, 2015 11:10 AM PDT
Current Scientific Events