2025 Cheriton Research Symposium

Continuous Integration and Delivery (CI/CD) pipelines process change sets that modify system behaviour by (1) invoking build and test routines, providing timely feedback to team members about whether changes integrate cleanly; (2) updating deployment environments with new system behaviour; and (3) exposing new system behaviour to samples of a user population while monitoring and responding to changes in operational metrics. CI/CD pipelines are composed of software artifacts, and as such, are prone to imperfections, such as noise (e.g., misleading signals from CI/CD) and waste (e.g., invocations of the pipeline that do not provide value). In this talk, I will present research that characterizes and mitigates noise and waste in CI/CD pipelines, and present avenues for future work.

Toshiya Hachisuka, Cheriton Faculty Fellow | DC 1302

Monte Carlo Methods for Partial Differential Equations

The core idea of Monte Carlo methods is to use repeated random sampling to obtain a numerical solution to a given problem. A prominent use case is photorealistic image synthesis in computer graphics, where Monte Carlo sampling and integration of light transport paths solve light transport simulation. Recently, my group has revisited the idea of using Monte Carlo methods to numerically solve partial differential equations. The conventional numerical solvers for partial differential equations start with approximating the continuous form of equations into a discrete form to derive numerical solutions out of matrix equations. The Monte Carlo approach fundamentally differs from this conventional approach in that one does not start with a discrete approximation but directly formulates a solution as an average of repeated random evaluations. It also enables us to leverage various Monte Carlo techniques to accelerate the numerical computation of deterministic partial differential equations, which are otherwise considered irrelevant. I will discuss this exciting research direction and demonstrate how the numerical solution to the Navier-Stokes equations, governing fluid dynamics, can be obtained by averaging random evaluations.

Craig S. Kaplan, Marsland Fellow | DC 1302

Aperiodic Tilings and the Einstein Problem

A set of shapes is an aperiodic tile set if the shapes admit tilings of the plane, but none with periodic symmetry.  Aperiodic tilings were initially conjectured to be impossible in the early 1960s, but the first aperiodic tile sets were found soon after.  Mathematicians discovered a sequence of ever smaller sets over a period of about ten years, but progress stalled after Penrose introduced the Kite and Dart, an aperiodic set of size two, in the 1970s.  The longstanding question of whether a single shape could tile the plane aperiodically became known as the einstein problem.  In 2023 I helped settle the einstein problem in collaboration with Smith, Myers, and Goodman-Strauss: we proved that a shape called the “hat” was an aperiodic monotile.  Separately we proved that related shapes called “spectres” could tile aperiodically without reflections.  I will talk about the history of aperiodic tilings, including some connections between tilings and computation, and relate the story behind the discovery of hats and spectres.

Lunch | DC 1301 (fishbowl)

By invitation