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We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization…
In view of the Segal construction each category with a coherent operation gives rise to a cohomology theory. Similarly each open stable differential relation $R$ imposed on smooth maps of manifolds determines cohomology theories $k^*$ and…
The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all…
A scheme for dynamical stabilization of entanglement quantified by the quantum Fisher information is analyzed numerically and analytically for bimodal and spin-1 Bose-Einstein condensates in the context of atomic interferometry. The scheme…
We consider $\mathcal{N}=4$ supersymmetric gauge theories on the squashed three-sphere with six preserved supercharges. We first discuss how Wilson and vortex loops preserve up to four of the supercharges and we find squashing independence…
We generalize the nonabelian Poincare duality theorems of Salvatore in [Sal01] and Lurie in [Lur09] to the case of not necessarily grouplike E_n-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's…
We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging…
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the…
We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review…
We summarize the usual implementations of the large $N$ limit of $O(N)$ models and show in detail why and how they can miss some physically important fixed points when they become singular in the limit $N\to\infty$. Using Wilson's…
We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used…
Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification.…
We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror…
We systematically construct the geometries dual to the 1+1 dimensional (0,4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S^1 x CY_3 compactifications of M-theory. This includes a large number of…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…
We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for an arbitrary compact semisimple gauge group in the so-called regular case. By this we mean the equations obtained…
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as…
We study charged scalar perturbations of charged extremal black holes in Einstein-Born-Infeld theory. Our numerical results indicate that these black holes all suffer from superradiant instability by the unstable quasi-bound states,…
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…