Group Theory
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Paper Amenability, unitarizability, and strong Ulam stability
Resolves Dixmier's problem for all discrete groups: amenability is equivalent to every uniformly bounded Hilbert-space representation being similar to a unitary representation. For countable discrete groups, amenability…
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Paper A hyperbolic group without a geometric CAT(0) action
Answers negatively whether every word-hyperbolic group is a CAT(0) group. Constructs one with a finite classifying space but no proper cocompact isometric action on any proper complete $`\mathop{\mathrm{CAT}}\nolimits…
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Paper Boone–Higman embeddings with higher finiteness
A finitely generated group has decidable word problem exactly when it embeds in a finitely presented simple group, proving the Boone–Higman conjecture. The target can have type F∞: a classifying space with finitely many…
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Paper Classifying spaces and geometric obstructions for Artin groups
The Salvetti complex of every finite-rank Artin group is aspherical, proving the Artin K(\pi,1) conjecture. Arbitrary intersections of its parabolic subgroups are parabolic, proving the Parabolic Intersection…
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Paper Thompson's group F is nonamenable
Proves that Thompson's group F, the group of dyadic piecewise linear homeomorphisms of the interval, is nonamenable, resolving its longstanding amenability problem. () Manuscript September 23, 2026 · · Lean…
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Paper An infinite finitely presented simple amenable group
Constructs an infinite finitely presented simple amenable group, answering the longstanding question of whether these properties can occur simultaneously. () Manuscript September 23, 2026 · · Lean formalization…
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Paper A torsion-free hyperbolic group that is neither residually finite nor linear over any field
Constructs a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question negatively. One fixed nonidentity element is killed by every finite-dimensional linear…
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