I am currently working on developing a theory of cellular sheaves for chemical reaction networks, I would love to talk about this with anyone that is interested. Here below, I have some of my research projects that I have been involved in:

Tetris Random Deposition

This Python package offers a suite of tools designed for simulating various random surface growth models. The foundational concepts and methodologies are significantly influenced by the work presented in the book by Barabási and Stanley [BarabasiS95] (1995) on fractal concepts in surface growth.

It is known that the fluctuations in the surface growth models fall into a few universality classes. The most famous one is the Kardar-Parisi-Zhang (KPZ) equation Kardar et al. [KPZ86]

$\frac{\partial h(t,x)}{\partial t}=\nu {\mathrm{\nabla }}^{2}h(t,x)+\frac{\lambda }{2}((\mathrm{\nabla }h(t,x){)}^2+\eta (t,x),t>0,x\in \mathbb{R},$

Where $\eta$ is a centered Gaussian noise, which is white in both space and time. The KPZ equation is a stochastic partial differential equation (SPDE)

Despite the variations in the type of surface growth that can occur, the growth of the first Betti number, ${\beta }_1$, is roughly linear from computational experiments.

There was a talk given on our work at the AMS Southeastern Sectional Meeting in 2024.