- Perfect State Transfer in Laplacian Quantum Walk: https://arxiv.org/abs/1409.5840
- An Explicit Construction of a Regular Model of a Hyperelliptic Curve in Mixed Characteristic (0, 2): in progress
- The reduced special fiber of any potentially semistable model is semistable: in progress; joint with Andrew Obus & Stefan Wewers
- Topological Obstructions to the Existence of a Resolution of the Singularities of a Variety: in progress
- An(other) Algorithm to Resolve the Singularities of a Curve: in progress; joint with Raymond van Bommel & Michael Montoro
- What Makes Quantum Computation Actually Quantum? An Extension of the Gottesman-Knill Theorem: Beyond the Clifford Gates? in progress; joint with Gilyana Dorzhieva, Jason Michael Perez, Josiah Sugarman, & Henry Todorow
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