My research centers on applications of dynamical systems to problems arising in population biology, fluid mechanics, and cancer biology. I use analytical methods and numerical tools from various fields of differential equations such as geometric singular perturbation theory, canard theory, bifurcation analysis, asymptotic analysis, stochastic differential equations, and reaction-diffusion systems of equations to study problems motivated by questions in physics and biology. My current work includes formulating and analyzing mathematical models, often featuring multiple timescales, to understand a broad range of questions in ecology, ranging from the role of trophic interactions in food-webs in shaping complex ecological dynamics to identifying early warning signals of sudden outbreaks and large-scale population fluctuations, and detecting regime shifts that may produce abrupt ecological transitions resulting in population collapse or community reorganization. In addition, I am also interested in studying boundary value problems (BVPs) on finite and infinite domains. The primary questions of interest are existence and multiplicity of solutions, asymptotic behaviors of solutions in case there are multiple solutions on an infinite domain, and deriving uniform asymptotic expansions of solutions in singularly perturbed BVPs as the singular parameter approaches zero.