We study a particular PDE model for chemotaxis with logarithmic sensitivity and logistic growth. We obtain existence and uniqueness of solutions as well as results for the zero-diffusion limit of the solutions with Neumann boundary conditions. We also show the formation of a boundary layer for the problem with dynamic boundary conditions, as well as some stability results. Numerical simulations will bring some light about the time-scale parameters as well as possible extensions on the problem. This is joint work with Kyle Zhao, Vincent Martinez and Ricardo Cortez. https://cuboulder.zoom.us/j/96510976623

A PDE model for chemotaxis with logarithmic sensitivity and logistic growth

Thu, Oct. 7 3pm (Zoom)

Probability

Evgeni S. Dimitrov (Columbia University)

X

Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability.

Gibbsian line ensembles can be thought of as collections of finite or countably infinite independent random walkers whose distribution is reweighed by the sum of local interactions between the walkers. I will discuss some recent progress in the asymptotic study of Gibbsian line ensembles, summarizing some joint works with Barraquand, Corwin, Matetski, Wu and others.

Beta-corners processes are Gibbs measures on triangular arrays of interacting particles and can be thought of as analogues/extensions of multi-level spectral measures of random matrices. I will discuss some recent progress on establishing the global asymptotic behavior of beta-corners processes, summarizing some joint works with Das and Knizel.

Gibbsian line ensembles and beta-corners processes