differentiable rendering of implicit surfaces

finding constructible completions of quilting patterns as they're being sketched

a low-level language (and exocompiler) designed to help performance engineers write, optimize, and target high-performance computing kernels onto new hardware accelerators

optimizing imperative array (tensor) code by rewriting functional programs in a verified way using Coq

handling automatic differentiation through discontinuous phenomena, such as collisions, boundaries, and phase changes

A mathematical theory of which quilt designs are constructable via a popular and easy to learn quilting process.

Why are Hardware Design Languages the way they are?

A Domain-Specific Hardware Design Language for trading off transistor usage (space) against pipeline latency (time)

correctness, brevity, and performance for complex geometric data structures

why should we bother designing new programming languages for physical simulation tasks?

a domain-specific language that automatically parallelizes code

exploring design variations while editing geometric patterns by inferring constraints

manipulating apparent objects in icon drawings

fast, efficient boolean library with a C interface

A freeform method for poking holes and merging surfaces

getting characters to turn on a dime, using non-parametric alternatives to motion graphs

robust boolean operations that are fast enough for interactive use.

knot theory meets graph theory. Hunting for the elusive minor minimal intrinsically knotted graphs