Joint Probability/Statistics and Math Finance Colloquium: A Kernel Framework for Linear Operator Equations

Event details Date: Wednesday, October 28, 2026 Time: 2:00 PM to 3:00 PM Location: Kaprielian Hall (KAP) - 414 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Valentin Tissot-Daguette, Bloomberg Title: A Kernel Framework for Linear Operator Equations Abstract: We present a Reproducing Kernel Hilbert Space (RKHS) framework for solving linear operator equations. By transferring the operator's action onto the kernel, these equations can be reduced to finite-dimensional ridge regressions. We also leverage random Nyström approximations to make implementations tractable while maintaining optimal convergence rates. Numerical experiments, notably on parabolic PIDEs, confirm the solver's accuracy and near-invariance to sample point selection. We conclude by constructing kernels on path spaces driven by transformer processes, paving the way for applications to path-dependent PDEs. Based on joint works with Damir Filipović (EPFL) and Josef Teichmann (ETH Zurich). Official event details: https://calendar.usc.edu/event/joint-probabilitystatistics-and-math-finance-colloquium-a-kernel-framework-for-linear-operator-equations