I am a mathematician and CEO of Pi1 Labs Inc, a company working on the interaction of AI with research in the basic sciences, particularly mathematics and physics. You may find my papers in mathematics here. I received my PhD from Princeton University in 2018 for work in algebraic geometry and homotopy theory, and completed my undergraduate studies at the University of Toronto. Previously, I was a researcher at SFB1085:Higher invariants and the Max Planck Institute for Mathematics in Bonn, and assistant professor of mathematics at the University of Southern California.
Email: mzargar [at] pi1labs [dot] com
Papers and Preprints:
Algebraic Geometry and Homotopy Theory
Comparison of Stable Homotopy Categories and a Generalized Suslin-Voevodsky Theorem, Advances in Mathematics, 354 (2019) .
Analytic number theory and Ramanujan graphs
Optimal strong approximation for quadrics over F_q[t]. Joint with N. Sardari. Advances in Mathematics, 413 (2023).
Ramanujan graphs and exponential sums over function fields. Joint with N. Sardari. Journal of Number Theory (2020).
Discrete mathematics via optimization
New upper bounds for spherical codes and packings. Joint with N. Sardari. Mathematische Annalen, 387 (2023).
The union-closed sets conjecture for non-uniform distributions, 2023.
Stiefel manifolds and upper bounds for spherical codes and packings, 2024.
Spectral geometry and equidistribution
Notes*:
*Not intended for publication.
