Zachary Stier

Email: zstier (at) berkeley (dot) edu.
I am a graduate student at UC Berkeley where I am fortunate to be advised by Nikhil Srivastava and supported by a NSF Graduate Research Fellowship. In 2020, I graduated from Princeton University where I was fortunate to be advised by Peter Sarnak for my senior thesis.

Papers and preprints

• I. Detherage, N. Srivastava, Z. Stier. "On the Ground State Energies of Discrete and Semiclassical Schrödinger Operators." 2024. In Pure and Applied Analysis and at arXiv:2405.05907.
• Z. Stier. "A no-go result for pure state synthesis in the DQC1 model." 2024. arXiv:2404.04198.
• A. Dawkins, V. Gupta, M. Kempton, W. Linz, J. Quail, H. Richman, Z. Stier. "A Ricci flow on graphs from effective resistance." 2024. arXiv:2403.01151. Submitted.
• A. Dawkins, V. Gupta, M. Kempton, W. Linz, J. Quail, H. Richman, Z. Stier. "Node resistance curvature in Cartesian graph products." 2024. arXiv:2403.01037. Submitted.
• Y. Borns-Weil, T. Saffat, Z. Stier. "A Quantum Algorithm for Functions of Multiple Commuting Hermitian Matrices." 2023. arXiv:2302.11139. Submitted.
• T. Blackman, Z. Stier. "Fast Navigation with Icosahedral Golden Gates." 2023. In Quantum Information and Computation and at arXiv:2205.03007.
• Z. Stier, J. Wellman, Z. Xu. "Dihedral Sieving on Cluster Complexes." 2021. In Enumerative Combinatorics and Applications and at arXiv:2011.11885.
• Z. Stier. "Short paths in PU(2)." 2021. In Quantum Information and Computation and at arXiv:2012.04695. (Part of my senior thesis.)
• Z. Stier. "Optimal topological generators of U(1)." 2020. In Journal of Number Theory and at arXiv:2002.03092. (Part of my senior thesis.)
• Q. Dao, N. Kenshur, F. Lin, C. Meng, Z. Stier, C. Yost-Wolff. "Metaplectic Analogues of Gelfand–Graev Models." 2019. REU report.
• Z. Stier. "A Proposed KDM-Secure Scheme to Evaluate k-DNF Formulas." 2019. Junior paper.
• D. Chait-Roth, A. Cui, Z. Stier. "A Taxonomy of Crystallographic Sphere Packings." 2019. In Journal of Number Theory and at arXiv:1903.03563.

Typesetting and exposition

• Notes on Lee–Yang-type theorems (based on notes by P. Srivastava and this paper by T. Asano).
• Nonbipartite LPS Ramanujan graphs (based on this paper by A. Lubotzky, R. Phillips, P. Sarnak)
• Quantum ergodicity on regular graphs (based on this paper by N. Anantharaman).
• P. Sarnak's letter about golden gates to S. Aaronson and A. Pollington: typeset PDF (original scan).

Seminar organization

• UC Berkeley student discrete analysis seminar: Spring 2022, Fall 2022, Spring 2023, Fall 2023, Fall 2024.
• Fall 2022 "roulette" student seminar on quantum theory.

My CV; some recent presentations; selected code.

I founded and direct YMath, a program that provides free tutoring in math to elementary, middle, and high school students in the Bergen County area who are unable to afford a private tutor.