Nicolas Lanchier
School of Mathematical
and Statistical Sciences
Arizona State University
Tempe, AZ 85287-1804

Office: WXLR 628
Email: nicolas.lanchier@asu.edu
Phone number: 480-965-3870

Curriculum Vitae
Ph.D. dissertation:
Multicolor particle systems

Pour les francophones ...
Cyrano a de grandes oreilles

Most mathematical models introduced in the life and social sciences literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations. These models, however, leave out any spatial structure or stochastic component while past research has identified space and stochasticity as key factors in how communities are shaped, and spatial stochastic models can result in predictions that strongly differ from their nonspatial deterministic counterparts. In contrast, my research aims at understanding the role of space and stochasticity in a wide variety of applied sciences such as physics, biology, sociology, economics, etc. through the mathematical analysis of a class of stochastic processes known as interacting particle systems. In these models, members of the population~(particles) such as atoms, cells, plants, voters, players, etc. are located on the vertex set of a connected graph. The latter has to be thought of as a network of interactions that dictates the dynamics of the system as particles can only interact locally with their neighbors, thus modeling the presence of an explicit spatial structure. Space in the context of interacting particle systems must be understood in a broad sense: an edge between two vertices of the underlying graph may be synonymous of geographic proximity, but also friendship relation, adherence to the same political party, etc. The main objective of research in this field is to understand the macroscopic behavior and spatial patterns that emerge from the microscopic interactions that describe the dynamics of large systems.