Related papers: The metaplectic correction in geometric quantizati…

We review our work of the past decade on one-loop quantum corrections to the mass M and central charge Z of solitons in supersymmetric field theories: the kink, the vortex, and the monopoles (focussing on the kink and the monopoles here).…

We show that quartic modifications of relativistic dispersion relations arise generically from deformation-quantized phase spaces under minimal kinematical assumptions relevant to quantum gravity. When the kinematics admits an integral…

A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…

We study properties of boundary conditions (BCs) in theories with categorical (or non-invertible) symmetries. We describe how the transformation properties, or (generalized) charges, of BCs are captured by topological BCs of Symmetry…

Let $K$ be a composite field of some real quadratic fields. We give a sufficient condition on $K$ such that all elliptic curves over $K$ is modular.

Within the paradigm of metamaterials and metasurfaces, electromagnetic properties of composite materials can be engineered by shaping or modulating their constituents, so-called meta-atoms. Synthesis and analysis of complex-shape meta-atoms…

Let $(M,\omega)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are…

In this note we apply a 4-fold sum operation to develop an associativity rule for the pairwise symplectic sum. This allows us to show that certain diffeomorphic symplectic $4$-manifolds made out of elliptic surfaces are in fact…

By working in a symplectically covariant real formulation of special K\"ahler geometry, we propose and give strong evidence for a canonical BPS partition function for AdS$_2 \times_w M_2$ near-horizon geometries with arbitrary rotation and…

The evolution of computer-generated holography (CGH) algorithms has prompted significant improvements in the performances of holographic displays. Nonetheless, they start to encounter a limited degree of freedom in CGH optimization and…

We show that in crystalline insulators point group symmetry alone gives rise to a topological classification based on the quantization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the…

We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into…

The issue raised in this paper is classical in the sense of being ancient: which subset of 4X4 matrices should be accepted as physical Mueller matrices in polarization optics? Non-quantum entanglement between the polarization and spatial…

Logarithmic and $b$-tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singularities by reframing singular vector fields as well-behaved…

The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…

We argue the possibility of realization of a polarization insensitive all-optical switching in a planar metamaterial composed of a 4-fold periodic array of two concentric metal rings placed on a substrate of nonlinear material. It is…

We prove the BPS decomposition theorem (a.k.a. cohomological integrality theorem) decomposing the cohomology of smooth symmetric stacks into the Weyl-invariant part of the cohomological Hall induction of the intersection cohomology of good…

The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…

We define Hecke modifications of conformal blocks over affine Lie algebras at non-critical level by using the Hecke modifications of the underlying $G$-bundles. We show that this procedure is equivalent to the insertion of a twisted vacuum…

In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…