About

Lee DeVille is a Professor in the Department of Mathematics and the Illinois Institute for Universal Biology at the University of Illinois Urbana-Champaign. He currently serves as the Director of Graduate Studies in Mathematics. In addition to his primary appointment, he is an Affiliate Faculty member in the Institute for Genomic Biology, the Illinois Neuroscience Program, and Computational Science and Engineering. His research interests focus on stochastic analysis, differential equations, and dynamical systems. Throughout his career, DeVille has been recognized with several honors including the N. Tenney Peck Teaching Award in Mathematics in 2010, designation as a National Academy of Science Kavli Fellow in 2012, and the Campus Distinguished Promotion Award from the University of Illinois in 2013.

Research topics

• Physics
• Pure mathematics
• Mathematics
• Geometry
• Computer Science
• Combinatorics
• Mathematical physics
• Mathematical analysis

Selected publications

• 2. Supporting Faculty in Mentoring Students for Careers Beyond Academia by Lee DeVille, Tegan Emerson, Skip Garibaldi, Mary Lynn Reed, Talitha M. Washington, and Suzanne L. Weekes

  Notices of the American Mathematical Society · 2023-10-01

  articleOpen access1st authorCorresponding

  Career opportunities for mathematicians in business, gov- ernment, and industry have never been better. At the 2023 Joint Mathematics Meetings in Boston, MA, the AMS Com- mittee on the Profession sponsored a panel entitled “Sup- porting Faculty in Mentoring Students for Careers Beyond Academia.” The goal of the panel was to provide action- able advice for faculty who seek to increase their ability to mentor students in finding nonacademic employment. To enable this information to reach a wider audience, we offer this interview-style report between our moderator and panelists.

  PublisherOA PDFDOI

• The shape of $x^2\bmod n$

  arXiv (Cornell University) · 2022-07-21

  preprintOpen access1st authorCorresponding

  We examine the graphs generated by the map $x\mapsto x^2\bmod n$ for various $n$, present some results on the structure of these graphs, and compute some very cool examples.

  PublisherOA PDFDOI

• Dynamical systems defined on simplicial complexes: symmetries, conjugacies, and invariant subspaces

  Chaos An Interdisciplinary Journal of Nonlinear Science · 2022 · 10 citations

  Senior authorCorresponding
  • Mathematics
  • Pure mathematics
  • Physics

  We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon, especially with regard to invariant subspaces in the dynamics.

  DOI

• Dynamical systems defined on simplicial complexes: Symmetries, conjugacies, and invariant subspaces

  Chaos An Interdisciplinary Journal of Nonlinear Science · 2022-09-01

  articleOpen accessSenior author

  We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon, especially with regard to invariant subspaces in the dynamics.

  PublisherOA PDFDOI

• Consensus on simplicial complexes: Results on stability and synchronization

  Chaos An Interdisciplinary Journal of Nonlinear Science · 2021 · 41 citations

  1st authorCorresponding
  • Computer Science
  • Mathematics
  • Computer Science

  We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian and show that it is a generalization of various consensus and synchronization models commonly studied on networks. In particular, our model allows us to formulate flows on simplices of any dimension so that it includes edge flows, triangle flows, etc. We show that the system can be represented as the gradient flow of an energy functional and use this to deduce the stability of various steady states of the model. Finally, we demonstrate that our model contains higher-dimensional analogs of structures seen in related network models.

  PublisherDOI

• Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian

  arXiv (Cornell University) · 2020-10-14 · 4 citations

  preprintOpen access1st authorCorresponding

  We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian, and show that it is a generalization of various consensus and synchronization models commonly studied on networks. In particular, our model allows us to formulate flows on simplices of any dimension, so that it includes edge flows, triangle flows, etc. We show that the system can be represented as the gradient flow of an energy functional, and use this to deduce the stability of various steady states of the model. Finally, we demonstrate that our model contains higher-dimensional analogues of structures seen in related network models.

  PublisherOA PDFDOI

• Circulant type formulas for the eigenvalues of linear network maps

  Linear Algebra and its Applications · 2020-09-25

  preprintOpen access1st authorCorresponding
  PublisherOA PDFDOI

• The generalized distance spectrum of a graph and applications

  Linear and Multilinear Algebra · 2020-08-16 · 2 citations

  preprintOpen access1st authorCorresponding

  The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many of the commonly studied spectra of graphs. We show that for a large class of graphs these eigenvalues can be computed explicitly. We also present the applications of our results to competition models in ecology and rapidly mixing Markov chains.

  PublisherOA PDFDOI

• Runge-Kutta and Networks

  arXiv (Cornell University) · 2019-08-29 · 1 citations

  preprintOpen access1st authorCorresponding

  We categorify the RK family of numerical integration methods (explicit and implicit). Namely we prove that if a pair of ODEs are related by an affine map then the corresponding discrete time dynamical systems are also related by the map. We show that in practice this works well when the pairs of related ODEs come from the coupled cell networks formalism and, more generally, from fibrations of networks of manifolds.

  PublisherOA PDFDOI

• Optimizing Gershgorin for symmetric matrices

  Linear Algebra and its Applications · 2019-05-03 · 1 citations

  preprintOpen access1st authorCorresponding
  PublisherOA PDFDOI

Recent grants

• CMG: Coarse-graining and Multiscale Analysis of Stochastic Particle-resolved Aerosol Models

  NSF · $773k · 2009–2014

Frequent coauthors

• Jared C. Bronski

  11 shared

• Sairaj V. Dhople

  6 shared

• Eugene Lerman

  6 shared

• Alejandro D. Domínguez-García

  5 shared

• Eddie Nijholt

  5 shared

• Timothy Ferguson

  Arizona State University

  4 shared

• Bard Ermentrout

  University of Pittsburgh

  4 shared

• Yi Zeng

  3 shared

Awards & honors

• N. Tenney Peck Teaching Award in Mathematics, 2010
• National Academy of Science Kavli Fellow, 2012
• Campus Distinguished Promotion Award, University of Illinois…