Title: A Stochastic Calculus Approach to Boltzman Transport 

Abstract: Oftentimes in life, we find a way to use one piece of information to achieve two or more outcomes. We are efficient. This principle is mirrored in literature, where revealing one truth often leads to additional insight. Consider Alexandre Dumas’ The Count of Monte Cristo: Edmond’s discovery of the treasure both provides him with immense wealth and societal influence while simultaneously enabling him to uncover the true nature of those who betrayed him.  As in life and art, so in math: this talk will show how to use a single set of Monte Carlo trajectories, or counts, to calculate both the solution to the Boltzmann transport equation and its adjoint.  Specifically, we will review source iteration, the canonical derivation of transport Monte Carlo, and reframe its method using stochastic calculus. By employing a Feynman-Kac style result, we prove that a single stochastic process lies at the heart of transport and adjoint transport. Consequently, Monte Carlo transport codes could potentially double their efficiency, transforming our approach to Boltzmann transport problems.