Daniel Lacker works at the intersection of applied probability, stochastic analysis, and mathematical finance. His primary research areas—mean field game theory and interacting particle systems—form the mathematical foundation for a wide range of models of large-scale systems of interacting agents. This modeling framework originated in statistical physics and, more recently, has been adapted to serve a variety of applications in the social sciences, such as financial markets, income inequality, and pedestrian crowd dynamics.
It is common in physics to approximate a large collection of discrete particles, such as those constituting a fluid, by modeling a continuum of particles. Continuous models are often much easier to analyze or simulate, and this approximation procedure has been made mathematically rigorous. On the other hand, recent extensions of these models for social scientific applications are not yet well understood. A main objective of Daniel’s research is to mathematically justify and quantify these ubiquitous “mean field” approximations as they arise in new and increasingly complex areas of application, particularly game theory.
Daniel was an NSF postdoctoral fellow in the Division of Applied Mathematics at Brown University from 2015-2017. He received his PhD from Princeton University in 2015 and his BS from Carnegie Mellon University in 2010, and in 2015 he was an Invited Fellow at the Institute for Pure and Applied Mathematics Program on Broad Perspectives and New Directions in Financial Mathematics.