Research

Our work may be broadly divided into biological and statistical, although there is often some overlap. Topics of interest include:

1. Growth and form in nature, e.g., morphological transitions, DNA conformations.

2. Collective behavior, e.g., cell dynamics and shape, foraging of ants.

3. Applications of artificial intelligence (AI) in biology, e.g., topological data analysis, deep learning.

4. Complex networks, e.g., social, traffic, control theory.

5. Mathematical framework for non-equilibrium/stochastic phenomena, e.g., Brownian dynamics, Fokker Planck equation.

Our approach is interdisciplinary, using a confluence of ideas from statistical physics (e.g., free energy, partition function), non-equilibrium physics (e.g. stochastic differential equations, self-organized criticality), differential geometry (e.g., curvature, metric), topology (e.g., linking number, genus), elasticity (e.g., bending, stretching, and twisting), probability (e.g., Fokker-Planck equation), nonlinear dynamics (e.g., reaction-diffusion equation), continuum mechanics (e.g., stress and strain), network science (e.g. nodes and links), artificial intelligence (e.g., machine learning, deep learning),  algebraic topology (e.g., Betti number, Forman-Ricci curvature), etc.