• Random structures induced by Laplacian determinants (spanning trees, unicycles, abelian sandpiles). See this version delivered in Bielefeld in Fall '18.
• Stochastic differential equations, with a focus on gradient models and Gibbs measures. Oodles of applications to statistical physics (spin systems under Glauber dynamics) and machine learning (stochastic gradient descent). Under development
• Interacting particle systems, coarse-graining lemmas, and the potential analysis thereof. (These are geared toward a specialized audience, probably not suitable for undergraduates.) Always under development in lockstep with my research progress
Information is posted on the Colgate Moodle for registered students.
From 2016 through 2022---with the exception of 2018-19---I served as the actuarial exam advisor for Colgate undergrads.
Exam info: Probability & Financial Math.
To take Exam P, you need a solid knowledge of calculus-based probability at the level of MATH 316, which is offered every fall.
My Exam P impressions + advice (November 2016).
Colgate does not offer a course that prepares for Exam FM, but a study guide (Broverman) is available at the Case-Geyer Library.