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Andrew V. Sutherland works in computational number theory and arithmetic geometry. His research includes algorithms for elliptic curves, their torsion subgroups, and explicit computations with modular curves. These subjects turn structural questions about equations over number fields into computations that can test and sharpen conjectures in number theory.^[ref]

Homepage: math.mit.edu/~drew/

Annette Huber, identified as Annette Huber-Klawitter on her institutional page, works in number theory and arithmetic geometry.^[ref] With Guido Kings and Niko Naumann, she developed integral and extension-field refinements of the Lazard isomorphism, relating continuous group cohomology to Lie algebra cohomology under stated hypotheses.^[ref]

The scientific use is a change of language: one can study suitable cohomology classes of a $p$-adic analytic group using alternating multilinear maps on its Lie algebra. Retaining integral coefficients is an extra achievement because passing to rational coefficients loses torsion elements information. The hypotheses in the comparison are therefore essential, rather than cosmetic generality.

Guido Kings is a mathematician working in number theory working in arithmetic geometry. In joint work with Annette Huber and Niko Naumann, he extended the Lazard isomorphism in two directions: to integral coefficients under additional hypotheses, and to analytic cochains over finite extensions $K/{\mathbb{Q}}_p$ compared with $K$-Lie algebra cohomology.^[ref]

This comparison replaces cohomological questions about a locally analytic group by questions about its infinitesimal Lie algebra, where linear and multilinear calculations are available. The base field matters: being analytic over $K$ is more restrictive than merely being analytic over ${\mathbb{Q}}_p$. His University of Regensburg page identifies his mathematical position and links to his research.^[ref]

Matthew Emerton is a mathematician working in number theory whose work connects modular forms, representation theory and arithmetic geometry. His authored account of classical modular forms as automorphic forms gives a precise translation between a weight-$k$ holomorphic function on the upper half-plane and an arithmetically invariant function on an adelic group.^[ref]

The translation converts a transformation rule into invariance and differentiation conditions. In particular, being holomorphic becomes annihilation by a suitable differential operator, while the weight becomes a character under rotations. This places classical modular forms in the same representation-theoretic language as more general smooth automorphic forms. His author page provides the note and identifies his research area as number theory.^[ref]

Niko Naumann works in arithmetic geometry and homotopy theory. With Annette Huber and Guido Kings, he refined the Lazard isomorphism, extending a comparison between continuous group cohomology and Lie algebra cohomology to integral coefficients under suitable hypotheses.^[ref]

The distinction between integral and rational coefficients matters: tensoring with ${\mathbb{Q}}_p$ can discard torsion elements, so a rational comparison does not automatically recover integral information. The same work also treats analytic cochains over finite extensions of ${\mathbb{Q}}_p$. Naumann's author page lists arithmetic algebraic geometry, motivic homotopy theory, and joint work on nilpotence and descent in equivariant stable homotopy theory.^[ref]