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A proof of the Donaldson–Thomas crepant resolution conjecture
Springer Science and Business Media LLC - Tập 229 - Trang 451-562 - 2022
We prove the crepant resolution conjecture for Donaldson–Thomas invariants of
hard Lefschetz 3-Calabi–Yau (CY3) orbifolds, formulated by Bryan–Cadman–Young,
interpreting the statement as an equality of rational functions. In order to do
so, we show that the generating series of stable pair invariants on any CY3
orbifold is the expansion of a rational function. As a corollary, we deduce a
symmetry ...
Bethe-Sommerfeld conjecture for periodic operators with strong perturbations
Springer Science and Business Media LLC - - 2010
Harmonic functions on planar and almost planar graphs and manifolds, via circle packings
Springer Science and Business Media LLC - Tập 126 - Trang 565-587 - 1996
The circle packing theorem is used to show that on any bounded valence transient
planar graph there exists a non constant, harmonic, bounded, Dirichlet function.
If $P$ is a bounded circle packing in ${\Bbb R}^2$ whose contacts graph is a
bounded valence triangulation of a disk, then, with probability $1$ , the simple
random walk on $P$ converges to a limit point. Moreover, in this situation any
c...
Concentration on the Boolean hypercube via pathwise stochastic analysis
Springer Science and Business Media LLC - Tập 230 Số 3 - Trang 935-994 - 2022
We develop a new technique for proving concentration inequalities which relate
the variance and influences of Boolean functions. Using this technique, we Our
proofs rely on techniques based on stochastic calculus, and bypass the use of
hypercontractivity common to previous proofs.
Mesures d’indépendance linéaire de logarithmes dans un groupe algébrique commutatif
Springer Science and Business Media LLC - Tập 162 - Trang 137-188 - 2005
This work falls within the theory of linear forms in logarithms over a connected
and commutative algebraic group, defined over the field of algebraic numbers
$\overline{\mathbb{Q}}$ . Let G be such a group. Let W be a hyperplane of the
tangent space at the origin of G, defined over $\overline{\mathbb{Q}}$ , and u
be a complex point of this tangent space, such that the image of u by the
exponential...
Einfacher Zusammenhang der Hilbertschemata von Kurven im komplex-projektiven Raum
Springer Science and Business Media LLC - Tập 99 - Trang 655-675 - 1990
Amalgams of Weyl algebras and theA (V, δ, Γ) conjecture
Springer Science and Business Media LLC - Tập 92 - Trang 163-171 - 1988
We prove a long standing conjecture ([5, Conjecture 5.6]) concerning the
algebrasA (V, δ, Γ). Namely, two such algebrasA (V, δ, Γ),A (W, ε, Ω) are
isomorphic if and only if there is an isomorphism between the ‘triples’ (V, δ,
Γ), (W, ε, Ω) from which they are constructed. As a consequence, to each
primitive ideal in the enveloping algebra of a solvable Lie algebra there is
associated a unique (V, ...
On the Forster-Eisenbud-Evans conjectures
Springer Science and Business Media LLC - Tập 46 - Trang 211-224 - 1978
Multiderivations of Coxeter arrangements
Springer Science and Business Media LLC - Tập 148 - Trang 659-674 - 2002
Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible
orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let
S be the algebra of polynomial functions on V. For H∈? choose α H ∈V * such that
H=ker(α H ). For each nonnegative integer m, define the derivation module D (m)
(?)={θ∈Der S |θ(α H )∈Sα m H }. The module is known to be a free S-module of
ran...
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