This is a mini-review about generalized instantons of noncommutative gauge theories in
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …

Abstract Let (X, ω X∗) be a separated,− 2–shifted symplectic derived ℂ–scheme, in the
sense of Pantev, Toën, Vezzosi and Vaquié (2013), of complex virtual dimension vdim ℂ X …

Magnificent four Page 1 Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 505–534 DOI
10.4171/AIHPD/93 Magnificent four Nikita Nekrasov Abstract. We present a statistical …

Recently, Nekrasov discovered a new “genus” for Hilbert schemes of points on C 4. We
extend its definition to Hilbert schemes of curves and moduli spaces of stable pairs, and …

This paper is concerned with a non-compact GIT quotient of a vector space, in the presence
of an abelian group action and an equivariant regular function (potential) on the quotient …

Abstract Suppose (X, Ω, g) is a compact Spin (7)-manifold, eg a Riemannian 8-manifold with
holonomy Spin (7), or a Calabi–Yau 4-fold. Let G be U (m) or SU (m), and P→ X be a …

We study Hilbert schemes of points on a smooth projective Calabi–Yau 4-fold X. We define
DT 4 invariants by integrating the Euler class of a tautological vector bundle L [n] against the …

Let $ X $ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define
Donaldson-Thomas type deformation invariants ($ DT_ {4} $ invariants) by studying moduli …

Let $ G $ be a finite subgroup of $\mathrm {SU}(4) $ such that its elements have age at most
one. In the first part of this paper, we define $ K $-theoretic stable pair invariants on a …

Abstract In 2008, Klemm–Pandharipande defined Gopakumar–Vafa type invariants of a
Calabi–Yau 4-folds using Gromov–Witten theory. Recently, Cao–Maulik–Toda proposed a …