March 1-5, 2021
The workshop will bring together leaders in mathematics, statistics, and atmospheric sciences to confront grand climate challenges and their impacts. A major goal of the program will be to develop next-generation suites of science-driven mathematical and statistical tools and capabilities to address decision-relevant climate hazards and impacts.
Complex societal problems can be studied and modeled through the mathematical theory of Mean Field Games. Indeed MFGs are a mathematical modeling approach to stochastically evolving systems which involve a large number of indistinguishable rational agents that have the same optimization criteria. The theory of MFG is very lively and productive at the moment and several important results have been achieved that can be applied to engineering, economics, finance, social sciences, In this final workshop we present recent analytic, probabilistic and numerical advances in this theory.
Mean field theories, Mean Field Games, and Mean Field Control are theoretical concepts which can naturally be brought to bear in applications to financial engineering. The workshop will examine how they influenced the development of financial mathematics theoretical works and the implementation of financial engineering solutions to problems involving large ensembles of individuals or robots optimizing their behaviors in uncertain and complex environments.
The paradigm of Mean Field Games (MFG) has become a major connection between distributed decision-making and stochastic modeling. Starting out in the stochastic control literature, it is gaining rapid adoption across a range of industries. The objective of this workshop is to give a clear vision of how MFG tools are being used in practical settings, both in complement and in contrast to the usual methodologies. The workshop will gather researchers both from industry and universities and will focus on diverse application areas.
Interacting particle models are a powerful mathematical tool to model the behavior of large groups in economics as well as in the life and social sciences. Understanding the dynamics of these systems on different levels is of great importance, as it gives insights into the emergence of many complex phenomena. In this workshop we will focus on recent developments and emerging challenges in the derivation and analysis of these micro- and mean-field models. It will feature different perspectives and approaches to these challenges, by bringing together applied mathematicians working at the interfaces between statistics, social sciences and the life sciences.
This conference invites participants to present and discuss current research on models with the following features. The heterogeneous agents feature refers to agents solving dynamic problems subject to idiosyncratic random shocks, each agent with non-trivial interactions with the remaining agents. The “aggregate dynamics” feature refers to the focus on the understanding and characterization of the dynamics of the entire system, either itself subject to aggregate shock or as a deterministic system, using analytical or numerical techniques. Examples of such models are variants of Mean Field Games. Models will have applications in several fields in economics and intersections with other disciplines.
The aim of this workshop is to gather specialists from machine learning and statistics to applied probability and analysis who share a common interest in mean-field models. Potential applications range from mean-field games to stochastic algorithms and simulations, neural networks and frequentist or Bayesian statistical inference for interacting systems.
This conference will consist of three series of lectures, the aim of which is to present the main issues at stake in the analysis of distributed solutions to complex societal problems and to describe some mathematical tools to handle these questions. Applications range from collective behavior in economy and finance to crowd analysis and the spread of diseases, and from machine learning to stochastic optimization and artificial intelligence.
With the advent of terascale, petascale and beyond computational capabilities, the reach of computational sciences is rapidly broadening well beyond its traditional ‘homes’ of physics, chemistry and computational engineering sciences to the biological and social sciences. To the extent to which such modeling and simulation are meant to be predictive in nature – and to the extent to which the systems being simulated are complex in nature – obvious questions regarding the veracity of the computational results must be inevitably confronted.
Modern machine learning methods have demonstrated an unprecedented potential to solve challenging problems in many areas. However, foundational understanding regarding how and when certain methods are adequate to use and most effective in solving tasks of interest is still emerging. A central question at the heart of this endeavor is to understand the different facets of the complexity of machine learning tasks.