Related papers: Perverse Results on Milnor Fibers inside Parameter…
This article introduces an approach that could tame wireless channels, making their behavior deterministic and software-defined. We investigate the novel idea of HyperSurfaces, which are software-controlled metamaterials embedded in any…
We theoretically demonstrated and experimentally verified high-order radial spoof localized surface plasmon resonances supported by textured metal particles. Through an effective medium theory and exact numerical simulations, we show the…
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained…
Optically resonant high-index dielectric metasurfaces featuring Mie-type electric and magnetic resonances are usually fabricated by means of planar technologies, which limit the degrees of freedom in tunability and scalability of the…
We study a class of skew products with overlaps in fibers and show that in this case the unstable manifolds really depend on prehistories, even for perturbations of the original maps. We also give several results about the Hausdorff…
We consider some nonlinear phenomena in metamaterials with negative refractive index properties. Our consideration includes a survey of previously known results as well as identification of the phenomena that are important for applications…
The existence of closed hypersurfaces of prescribed curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…
We introduce Veronese-Avoiding hypersurfaces, inspired by the theory of associated forms of Alper--Isaev. In the smooth case, we reinterpret their criterion via Macaulay inverse systems: the Veronese-Avoiding condition is equivalent to the…
We provide a description of Iwahori-Whittaker equivariant perverse sheaves on affine flag varieties associated to tamely ramified reductive groups, in terms of Langlands dual data. This extends the work of Arkhipov-Bezrukavnikov from the…
We extend a result of to Esnault-Levine-Viehweg concerning the Chow groups of hypersurfaces in projective space to those in weighted projective spaces.
We study extension of scalars for sheaves of vector spaces, assembling results that follow from well-known statements about vector spaces, but also developing some complements. In particular, we formulate Galois descent in this context, and…
We discuss the behavior of a crystalline surface with a disordered substrate. We focus on the possible existence of a {\em super-rough} glassy phase, with height-height correlation functions which vary as the square logarithm of the…
We classify isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$ and thereby reprove a result of Dorfmeister and Neher.
In this work we study analytic Levi-flat hypersurfaces in complex algebraic surfaces. First, we show that if this foliation admits chaotic dynamics (i.e. if it does not admit a transverse invariant measure), then the connected components of…
This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…
We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…
This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up of a projective surface at a point. The followings are main results of this…
Metasurfaces, ultrathin and planar electromagnetic devices with sub-wavelength unit cells, have recently attracted enormous attention for their powerful control over electromagnetic waves, from microwave to visible range. With tunability…
We describe the perverse filtration in cohomology using the Lefschetz Hyperplane Theorem.