Scientists / Open questions
Maryam Mirzakhani
Hyperbolic geometry; moduli spaces; dynamical systems
2014 Fields Medal
9 questions
Weil-Petersson volume asymptotics in the mixed regime of large genus and growing number of boundary components, and large-degree coefficients of the volume polynomials
Universality of the bottom of the length spectrum: finding an a priori mechanism relating Weil-Petersson and combinatorial models of random surfaces
Robustness of hybrid monolayer-bilayer graphene quantum dot energy spectra to realistic edge terminations, dot shape, and atomistic boundary structure
Long-term performance, mechanisms, economics, and residue-management optimization of organic rice–wheat and rice–wheat–mungbean systems with crop residue incorporation in the Indo-Gangetic Plains
Removing the polynomial prefactor from the finite-time lattice count in strata (Theorem 5.1 of Eskin–Mirzakhani–Rafi)
Sharp error terms and uniformity in the centers in the Teichmuller lattice point and volume asymptotics
A Mirzakhani-style volume and intersection theory for the SU(2) character varieties of bordered surfaces with fixed boundary holonomy
The universal constant and the critical many-markings regime in the Mirzakhani-Zograf large-genus asymptotics of Weil-Petersson volumes
Rigorous semiclassical theory of moiré-induced potential wells in twisted bilayer graphene quantum dots