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Andrei Seymour-Howell works in computational number theory, particularly automorphic forms and trace formulas. His 2022 paper develops an algorithm to compute and rigorously verify Maass cusp forms for specified groups of squarefree level and trivial character. It combines a Selberg trace formula involving Hecke operators with linear algebra to isolate spectral information.^[ref]

The distinction between computation and certification is central. A decimal approximation to an eigenvalue suggests where to look; a rigorous verification must justify that the computed information corresponds to an actual mathematical object, with controlled error. As a schematic illustration, a proved enclosure $9.99\le \lambda \le 10.01$ conveys a different kind of information from a program merely printing 10.00. The numbers here illustrate the distinction and are not a reported eigenvalue. The paper applies its verified computations to gather evidence about further conjectures; verified examples still do not prove a conjecture quantified over all forms.^[ref]