Related papers: Meanders, hyperelliptic pillowcase covers, and the…
We build polyhedral complexes in Rn that coincide with dyadic grids with different orientations, while keeping uniform lower bounds (depending only on n) on the flatness of the added polyhedrons including their subfaces in all dimensions.…
We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…
In this paper, we show an inequality between the degrees of the conductor and the Hodge fiber of a hyperelliptic curve above a discrete valuation ring. For that we have to show theorems about the lifting of $p$-cyclic covers in order to…
We introduce filtrations in chiral homology complexes of smooth elliptic curves, exploiting the mixed Hodge structure on cohomology groups of configuration spaces. We use these to relate the chiral homology of a smooth elliptic curve with…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
This is the second of a series of two papers where we construct embedded Willmore tori with small area constraint in Riemannian three-manifolds. In both papers the construction relies on a Lyapunov-Schmidt reduction, the difficulty being…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
For each large enough $m\in\mathbb{N}$ we construct by PDE gluing methods a closed embedded smooth minimal hypersurface ${\breve{M}_m}$ doubling the equatorial three-sphere $\mathbb{S}_{\mathrm{eq}}^3$ in $\mathbb{S}^4(1)$, with…
We construct most symmetric Saddle towers in Heisenberg space i.e. periodic minimal surfaces that can be seen as the desingularization of vertical planes intersecting equiangularly. The key point is the construction of a suitable barrier to…
This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Johnson kernel. Second, we show that the Johnson filtration…
Fabrication of sub-micron Josephson junctions is demonstrated using standard processing techniques for high-coherence, superconducting qubits. These junctions are made in two separate lithography steps with normal-angle evaporation. Most…
Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary…
Josephson junctions are key elements in superconducting electronics. The most common type is the overlap (sandwich-type) junction, formed by vertically stacking two superconducting layers. In contrast, planar junctions are fabricated…
A variety of electrostatic phenomena, including the structure of electric double layers and the aggregation of charged colloids and proteins, are affected by nonuniform electric permittivity. These effects are frequently ignored in…
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to…
Identifying parallel sides of a collection of Euclidean polygons yields a flat surface with cone points of angles multiples of 2 pi, naturally a compact Riemann surface but also an algebraic curve, and a hyperbolic surface. In general two…
Hypothesis: Colloidal molecules with anisotropic shapes and interactions are powerful model systems for deciphering the behavior of real molecules and building units for creating materials with designed properties. While many strategies for…
The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated…
We construct small covers and quasitoric manifolds over $n$-dimensional simple polytopes which allow proper colorings of facets with $n$ colors. We calculate Stiefel-Whitney classes of these manifolds as obstructions to immersions and…
Waveguides are critically important components in microwave, THz, and optical technologies. Due to recent progress in two-dimensional materials, metasurfaces can be efficiently used to design novel waveguide structures which confine the…