Related papers: Perverse Results on Milnor Fibers inside Parameter…
Enhanced ind-sheaves provide a suitable framework for the irregular Riemann-Hilbert correspondence. In this paper, we give some precisions on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we…
It is shown that the transparency of opaque material with negative permittivity exhibits resonant behavior. The resonance occurs as a result of the excitation of the surface waves at slab boundaries. Dramatic field amplification of the…
In this paper, we establish a general inequality for locally strongly convex centroaffine hypersurfaces in $\mathbb{R}^{n+1}$ involving the norm of the covariant derivatives of both the difference tensor $K$ and the Tchebychev vector field…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy K\"ahler moduli space (SKMS) associated by Halpern-Leistner and Sam to a…
We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. In particular we show that any projective hypersurface has affine parts which are bouquets of spheres. The main…
Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and band gap engineering, and are based on simple shapes with high degrees of symmetry. We show…
Recent investigations on optical nonlinearities of plasmonic materials suggest their responses may be even beyond the usual perturbative description. To better understand these surprisingly strong responses, we develop here a simple but…
The purpose of this paper is to compute the degree of irrationality of hypersurfaces of sufficiently high degree in various Fano varieties: quadrics, Grassmannians, products of projective space, cubic threefolds, cubic fourfolds, and…
This paper is a survey paper on old and recent results on direction problems in finite dimensional affine spaces over a finite field.
We introduce a new generalization of the notion of preperiodic hypersurface and explore some of its basic ramifications. We also prove that among nonlinear endomorphisms of projective space, those with a periodic critical point are Zariski…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
Transmission through a subwavelength terahertz fiber, which is positioned in parallel to a frequency selective surface, is studied using several finite element tools. Both the band diagram technique and the port-based scattering matrix…
We prove birational superrigidity of Fano cyclic covers of index 1 over hypersurfaces in the projective space.
We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P^m x P^n, we describe their nef, movable and effective cones and determine when they are Mori dream spaces. Using these…
We define a quantum analogue of the Grothendieck ring of finite dimensional modules of a quantum affine algebra of simply laced type. The construction is based on perverse sheaves on a variety related to quivers. We get also a new geometric…
Continuing the study of perverse sheaves on the nilpotent cone of a $\mathbb{Z}/m$-graded Lie algebra initiated by Lusztig--Yun, we study in this work the parabolic induction and introduce the notion of supercuspidal sheaves on the…
In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every…
The design of metamaterials which support unique optical responses is the basis for most thin-film nanophotonics applications. In practice this inverse design problem can be difficult to solve systematically due to the large design…
We analyse the fine convergence properties of one parameter families of hyperbolic metrics, on a fixed underlying surface, that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms.