Much of my work involves the Gunawardena lab’s linear framework, a graph-theoretic approach to Markov processes developed to model timescale separation in biochemical systems. For more mathematical details, please refer to this publication. In particular, I tend to use the linear framework to understand applications in stochastic thermodynamics.
Signatures of non-equilibrium steady-states
Detecting nonequilibrium behavior in biological information processing systems poses a technical challenge in experimental and theoretical contexts. To address this difficulty, several mathematical signatures of broken detailed balance in Markovian systems have been suggested. While these signatures identify the presence of energy expenditure, little is known about how they relate to underlying thermodynamic forces. Part of my PhD work has focused on characterizing the mathematical behavior of such signatures, which can elucidate new properties of nonequilibrium systems to be tested experimentally in real biological contexts.
Asymptotic graphs
I have also been interested in expanding the mathematical foundations of the linear framework, which has allowed me to explore more theoretical research questions using graph theory, applied linear algebra, spectral analysis, Markov processes, Riemannian geometry, algebraic topology, combinatorics, and category theory. In particular, we have developed a novel construction in graph theory that emerges when a particular edge label in a linear framework graph is taken to infinity.