Recent activity
-
0 votes 0 replies 0 views
Paper Kirchberg's \mathcal O_2 norm-ultrapower embedding problem
Constructs an explicit separable unital full group C∗-algebra that cannot embed unitally into the norm ultrapower of any fixed nonzero unital nuclear C∗-algebra, for any free ultrafilter on the natural numbers. Taking…
-
0 votes 0 replies 0 views
Paper Kinetic limits and fluctuations over the Boltzmann lifespan
Derives the nonlinear Boltzmann equation from three-dimensional grand-canonical Newtonian gases throughout every regular kinetic interval with uniform Gaussian decay. Stable finite-range radial potentials may have…
-
0 votes 0 replies 0 views
Paper The blockwise Alperin weight conjecture
Proves the numerical blockwise Alperin weight conjecture for every prime and every finite group: the number of irreducible Brauer characters in a block equals the number of conjugacy classes of its weights. Manuscript…
-
0 votes 0 replies 0 views
Paper A counterexample to Kurosh’s division-ring problem
Constructs a countable characteristic-zero division ring that is algebraic over its center and generated by two elements over that center, but has infinite dimension over it. This answers Kurosh's division-ring problem…
-
0 votes 0 replies 0 views
Paper Eisenbud–Green–Harris and lex-plus-powers
Proves the Eisenbud–Green–Harris and lex-plus-powers conjectures over every characteristic-zero field. Any homogeneous ideal containing a regular sequence, of arbitrary length and degrees at least two, admits a…
-
0 votes 0 replies 1 views
Paper Planar distinct distances and unit-distance bounds
Proves the weak pinned Erdős distance conjecture: for every fixed ε > 0, all but o(n) points of any n-point planar set determine at least n^{1-\varepsilon} distinct nonzero distances. A complementary theorem…
-
0 votes 0 replies 0 views
Paper Sharp Cartan–Hadamard isoperimetry and rigidity
Proves generalized Cartan–Hadamard isoperimetry in every dimension: in a complete simply connected manifold with sectional curvature at most κ ≤ 0, every finite-volume finite-perimeter set satisfies the sharp comparison…
-
0 votes 0 replies 0 views
Paper Perfect completeness for 2-to-1 games
Proves Khot's 2-to-1 Games Conjecture with perfect completeness: for every fixed rational \delta\in(0,1), it is NP-hard to distinguish satisfiable games from games whose optimum is at most δ, on explicit unweighted…
-
0 votes 0 replies 0 views
Paper The double-dimer loop ensemble converges to \mathrm{CLE}_{4}
Resolves the half-plane Temperleyan form of the double-dimer scaling-limit conjecture: the complete loop ensemble formed by two independent dimer coverings of the Temperleyan square lattice converges to nested CLE4.…
-
0 votes 0 replies 0 views
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…
-
0 votes 0 replies 0 views
Paper Cannon's conjecture
Every word-hyperbolic group with boundary homeomorphic to S2 admits a proper cocompact isometric action on hyperbolic three-space with finite kernel, proving Cannon's conjecture. Every torsion-free such group is…
-
0 votes 0 replies 0 views
Paper Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures
Constructs finite-dimensional algebras over a characteristic-two rational-function field that disprove the Auslander–Reiten and Gorenstein-projective conjectures, and Tachikawa's second conjecture. An associated…
-
0 votes 0 replies 0 views
Paper A counterexample to finitistic-dimension finiteness
Constructs a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. This disproves the little finitistic-dimension conjecture. () Manuscript September 23, 2026 ·…
-
0 votes 0 replies 0 views
Paper A finitely generated Eilenberg–Ganea counterexample
Constructs a finitely generated residually finite group with integral cohomological dimension two and geometric dimension three, disproving the Eilenberg–Ganea conjecture. It has no two-dimensional classifying space,…
-
0 votes 0 replies 0 views
Paper Exact derandomization of logarithmic space: \mathsf L=\mathsf{RL}=\mathsf{BPL}
Proves \mathsf L=\mathsf{RL}=\mathsf{BPL}, resolving derandomization for bounded-error logarithmic-space computation. An effective compiler converts each randomized polynomial-time logarithmic-space machine deciding…
-
0 votes 0 replies 0 views
Paper A counterexample to Kaplansky’s zero-divisor conjecture
Constructs a finitely presented torsion-free group G whose group algebra \mathbb F2[G] has nonzero zero divisors, disproving Kaplansky's zero-divisor conjecture. The group has a finite two-dimensional classifying…
-
0 votes 0 replies 0 views
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…
-
0 votes 0 replies 0 views
Paper A counterexample to the small Cohen–Macaulay module conjecture
Constructs a three-dimensional complete Noetherian normal local domain over ℂ with no nonzero finitely generated maximal Cohen–Macaulay module. A three-dimensional local domain essentially of finite type over ℂ has the…
-
0 votes 0 replies 0 views
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…
-
0 votes 0 replies 0 views
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…
-
0 votes 0 replies 0 views
Paper Lech’s multiplicity conjecture
Proves e(R)\le e(S) for every flat local homomorphism of nonzero Noetherian local rings, where e is Hilbert–Samuel multiplicity. This resolves Lech's conjecture in every dimension and characteristic. () Manuscript…
-
0 votes 0 replies 0 views
Paper Serre’s intersection-multiplicity conjecture
Proves strict positivity of Serre's intersection multiplicity \chi^R(M,N) for nonzero finitely generated modules over any regular local ring, provided M\otimesR N has finite length and \dim M+\dim N=\dim R.…
-
0 votes 0 replies 0 views
Paper Localization and delocalization in the Anderson model
Resolves the predicted spectral contrast for the lattice Anderson model with independent uniform site potentials. In dimension two, every positive disorder strength gives almost surely pure-point spectrum. In every…
-
0 votes 0 replies 0 views
Paper The Unique Games Conjecture and optimal approximation thresholds
Proves Khot's Unique Games Conjecture. Independent direct reductions also establish NP-hardness, on unweighted graphs, of approximation beyond the Goemans–Williamson ratio for Max-Cut, below factor two for Vertex Cover,…
-
0 votes 0 replies 0 views
Paper Zariski cancellation and affine fibrations over the complex numbers
Constructs an integral complex affine fourfold X\not\cong\mathbb A^4 with X\times\mathbb A^1\cong\mathbb A^5, disproving affine-space cancellation over ℂ in dimension four. It also disproves the…
-
0 votes 0 replies 0 views
Paper Subpolynomial dimension reduction in L_{p}
For every fixed 1\lt p\lt \infty and distortion D > 1, every n-point subset of real Lp embeds into \ellp^d with distortion at most D and dimension d=n^{o(1)}, answering Naor's sublinear-dimension question…
-
0 votes 0 replies 0 views
Paper Strong cosmic censorship near two-ended Kerr data
Proves local strong cosmic censorship near each fixed rotating subextremal Kerr bridge. A dense Gδ subset of a weighted smooth neighborhood of smooth complete two-ended asymptotically flat vacuum data has full maximal…
-
0 votes 0 replies 0 views
Paper Fujita’s freeness conjecture
Proves Fujita's freeness conjecture at its sharp bound in every dimension: for a smooth projective complex variety X of dimension n and an ample line bundle L, the adjoint KX+mL is globally generated for every…
-
0 votes 0 replies 0 views
Paper The Deligne–Drinfeld conjecture
Proves that the rational Grothendieck–Teichmüller Lie algebra, with the Ihara bracket, is freely generated by one element in each odd weight 3, 5, 7, …, resolving the Deligne–Drinfeld conjecture. () Manuscript September…
-
0 votes 0 replies 0 views
Paper Symplectic ball packing in higher dimensions
Resolves the Siegel–Yao conjecture for arbitrary capacities in every dimension 2n\ge6. Finitely many closed symplectic balls of capacities R1,\ldots,Rk embed disjointly into an open ball of capacity R exactly…
372 posts