Two tales of elliptic curves: cell modelling and algebraic K-theory

Date

Jun 18, 2026

Time

3:00 PM - 4:00 PM

Speaker

Xiao Yang

Affiliation

Leiden University

Language

en

Main Topic

Biologie

Host

Math Groups

Description

Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. A straightforward model is by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider also a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta measure located at the cell’s centre. The amplitude of the Dirac delta measure is a nonlocal term of the compound’s concentration near the virtual cell boundary so as to preserve the essential biological features. To investigate the positivity of the solution and the structure of steady states, we employ the Laplace transform. In addition, the theory of elliptic curve is also involved.

Last modified: Jun 18, 2026, 7:40:02 AM