Scientists / Open questions
Akshay Venkatesh
Number theory; automorphic forms; homogeneous dynamics
2018 Fields Medal
9 questions
The Ellenberg–Jain–Venkatesh random-matrix model for λ-invariants of imaginary quadratic fields: proving the equidistribution conjecture and its refinements
Schur-corrected counting of number fields: prove the predicted leading constant, secondary terms, and distribution laws for -extensions beyond the function-field theorems
The local-global principle for representations of quadratic forms in codimension two
Venkatesh's strong conjecture: closure of the Arthur-type unitary dual of GL(n) under restriction, induction, and tensor product
Michel–Venkatesh's questions from “The subconvexity problem for GL2”: subconvexity-inspired fast computation of central L-values, and the asymptotic count of cusp forms by analytic conductor
Optimal dependence on the ambient ternary form of the count of embeddings of a binary quadratic form
Unconditional pointwise bounds for -torsion in class groups of number fields toward the -torsion (-)conjecture: the regimes left open by the Ellenberg–Venkatesh reflection method
Unconditional concentration of reduced-basis counts, LLL/BKZ analogues, and predicting which reduced bases LLL outputs (open problems from Kim–Venkatesh, The Behavior of Random Reduced Bases)
Finite locally-quasiprimitive graphs: completing the Li–Praeger–Venkatesh–Zhou structure theory and the Weiss-type vertex-stabiliser bound