Our research investigates the mechanisms of learning and synaptic plasticity in the brain from a computational perspective. Example research directions that we are actively working on include: 1) How can synaptic plasticity induced by replay events and sleep help animals build a representation of their sensory environment? 2) What mechanisms does the brain use to rapidly recompose previously learned information to solve new tasks, without forgetting solutions to old tasks? 3) How do therapeutic interventions, like brain-computer interfaces and psychedelic drug administration interact with the brain’s learning mechanisms? To provide answers to these questions, we use mathematical tools from a diversity of fields, including optimization, machine learning, statistics, and dynamical systems, to build theories and data analysis tools that make sense of experimental learning data.