Direct proof of Danilov-type formula for toric origami manifolds.
problem Proving a Danilov-type formula for toric origami manifolds.
method Localization of Riemann-Roch number.
result Direct geometric proof of Danilov-type formula.
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48 results for “toric origami manifolds”
Origami structures are enumerated and shown to be quantum modular.
problem Counting and understanding origami structures with real structures.
method Using combinatorics of zonal polynomials and Schur polynomials, and relating to quantum modular forms and double Hurwitz numbers.
result The generating functions of certain origami structures are quantum modular forms.
Origami edge-paths connect coherent curves on surfaces.
problem Understanding coherent curves on surfaces.
method Origami structure and edge-paths.
result Existence of origami edge-paths connecting coherent curves.
Origami creates flat torus models of any size.
problem Creating flat torus models of any size.
method Explicit origami folding instructions.
result Flat torus models of any size created.
The paper calculates Veech groups and Galois invariants for general origamis.
problem Understanding the structure and symmetries of origamis and their Galois invariants.
method Developed an algorithm to calculate Veech groups and orbits of Galois invariants for general origamis.
result Calculated Veech groups and Galois invariants for all origamis of degree .
Unified theory solves strain compatibility and elasticity of origami metamaterials.
problem Understanding and controlling the morphing paths of origami metamaterials.
method Unified theory for a wide array of origami tessellations, solving strain compatibility and elasticity.
result Origami metamaterials exhibit equal but opposite in-plane and out-of-plane Poisson's ratios and bending energy depends on strain gradient.
Study of origamis in minimal stratum with single cylinders, calculating spin parities and monodromy groups.
problem Understanding the structure and properties of origamis in the minimal stratum of moduli space.
method Construction and analysis of minimal -origamis, calculation of spin parities, and investigation of monodromy groups.
result All minimal -origamis have monodromy groups that are almost always finite simple groups.
Finite groups can be represented as origami automorphisms, extended to countable groups.
problem Representing countable groups as automorphisms of origamis.
method Considering origamis on the Loch Ness monster.
result Every countable group can be represented as origami automorphisms.
New game defined on origami patterns, linking number introduced.
problem Defining a game on origami patterns.
method Introduced Region Select on origami crease patterns.
result Defined a new unlinking number.
Paper analyzes origami slope gaps and their distribution, finding a unique pattern.
problem Analyzing slope gaps in origami surfaces.
method Derived slope gap distribution of a specific origami by considering return times under the horocycle flow.
result Found a unique distribution of origami slope gaps, not a sum of scaled Hall distributions.
Origamis with specific groups have Veech groups that surject onto SL(2, Z/nZ).
problem Characterizing Veech groups of origamis as totally non-congruence groups.
method Using results on SL(2, Z/nZ) and properties of origamis' deck transformation groups.
result Origamis with certain triangle group quotients have Veech groups that surject onto SL(2, Z/nZ).
Origamis described using Schottky groups for surfaces of genus g ≥ 1.
problem Describing origamis by Schottky groups for Riemann surfaces.
method Using geometrical structural picture and Klein-Maskit combination theorems.
result Provided a geometrical structural picture of origami-Schottky groups.
The paper studies the index of a specific monodromy for origamis in a particular stratum.
problem Determining the index of a Kontsevich-Zorich monodromy for origamis in .
method Analyzing the action of the Veech group on the non-tautological part of the homology.
result The index of the Kontsevich-Zorich monodromy is either 1 or 3 for origamis in .
As main result we show that for each g > 1 there is some translation surface of genus g whose Veech group is a non congruence subgroup of SL(2,Z). We use origamis/square-tiled surfaces to produce our examples. The article is divided into two parts: In the first part we introduce translation surfaces, origamis, Veech gr…
Paper shows minimum 10 vertices for hyperbolic origami 2-torus.
problem Finding minimum vertices for hyperbolic origami 2-torus.
method Geodesic triangulation and isometric polyhedral embedding.
result 10 vertices are the minimum required for a hyperbolic origami 2-torus.
The study generalizes origamis to flat surfaces, exploring their combinatorial and geometric properties.
problem Understanding the geometric and combinatorial properties of flat surfaces.
method Developing a system of linear equations to represent flat surfaces and studying their Veech groups.
result Veech groups of certain flat surfaces are included under a specific covering relation.
We consider a rather special class of translation surfaces (called M-Origamis in this work) that are obtained from dessins by a construction introduced by Martin Möller. We give a new proof with a more combinatorial flavour of Möller's theorem that acts faithfully on the…
New expanders found using origami surfaces with spectral gap.
problem Constructing expanders with spectral gap on surfaces of arbitrary genus.
method Affine actions on origami surfaces to achieve spectral gap.
result New expanders distinct from classical ones.
Origami curves link surface automorphisms to group actions.
problem Realizing finite groups as automorphisms of origami curves.
method Proving the existence of origami pairs with equivalent actions.
result Finite groups can be realized as origami automorphisms.
Arithmetic Kontsevich-Zorich monodromy found in a specific origami surface.
problem Exploring the monodromy of a symmetric origami in genus 4.
method Analyzing the Veech group and symplectic group properties of the origami.
result Existence of arithmetic Kontsevich-Zorich monodromy in a specific origami.
Minimal hitting time on origami equals diophantine type for certain slopes.
problem Determining hitting time on origami surfaces.
method Analyzing hitting time and diophantine type on specific origami models.
result For genus 4 origami, hitting time equals diophantine type for certain slopes.
The paper characterizes Veech groups using origamis and flat surfaces.
problem Characterizing Veech groups in terms of origamis.
method Analysis of flat surfaces with two finite Jenkins-Strebel directions, using geodesics and parallelograms.
result Elements in the Veech group of a flat surface with two finite Jenkins-Strebel directions are characterized by a concurrence between two origamis.
Origami patterns are classified based on their symmetry groups.
problem Classifying the symmetry groups of origami patterns.
method Iteratively compute intersection points and lines to construct mathematical origami sets, then classify them based on wallpaper groups.
result Determine which wallpaper groups can be constructed from given origami patterns.
Origami uses SGX enclaves and blinding to protect deep neural network inference privacy.
problem Protecting deep neural network inference privacy in machine learning services.
method Combines enclave execution, cryptographic blinding, and accelerator-based computation.
result Demonstrates improved privacy-preserving inference performance compared to prior work.
Origami solves real cubic equations, revealing a specific curve.
problem Solving real cubic equations using origami.
method Investigating a specific real cubic curve and analyzing its properties.
result The shape of Beloch's curve is determined by the Hessian at its singular point.
Origami graphs' Euler characteristics grow as origami complexity increases.
problem Proving McMullen's conjecture about origami graphs' expansion properties.
method Counting integral and orbifold points on algebraic hypersurfaces, Teichmüller curves, and pseudo-Anosov diffeomorphisms.
result The absolute values of Euler characteristics go to infinity with origami complexity.
Strata of -Origamismath.GT
Study of origamis' singularities for groups of prime-power order.
problem Classifying singularities of origamis for groups of prime-power order.
method Geometric and group-theoretic ideas used to classify strata.
result Many groups of prime-power order have only one stratum, but some do not.
Toric Vaisman Manifoldsmath.DG
The paper explores toric Vaisman manifolds and their connections to Sasaki and Kähler geometry.
problem Understanding the geometric relationships between Vaisman, Sasaki, and Kähler manifolds in the toric context.
method Introducing and analyzing toric Vaisman structures, showing relationships between minimal coverings and associated Sasaki manifolds, and proving conditions for toricity.
result Toric Vaisman manifolds have a close relationship with toric Sasaki manifolds, and vice versa, under specific conditions.
We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…
Paper constructs a complex from flow data, capturing manifold's structure.
problem Understanding flows on manifolds with boundaries.
method Origami map from disk to CW-complex, reconstructing manifold's topology.
result Compact -complex homotopy equivalent to manifold .
Study systolic geometry of translation surfaces and origamis.
problem Investigate systolic ratios of translation surfaces and origamis.
method Analyze systoles and saddle connections, develop algorithm, compute ratios.
result Compute maximal systolic ratio of origamis in up to 67 squares.
Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
problem Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
method Filtration approach to prove the conjecture.
result Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
New insights into algebraic geometry of a conjecture, leading to origami curves.
problem Algebraic and geometric perspectives on the Putman-Wieland conjecture.
method Algebraic and geometric constructions of origami curves.
result Origami curves with high-dimensional isotrivial isogeny factors.
This paper provides a new method to construct -symplectic toric manifolds from toric manifolds.
problem Classifying and constructing -symplectic toric manifolds.
method A new method to construct -symplectic toric manifolds from toric manifolds.
result This new method allows for the decomposition of -symplectic toric manifolds into toric manifolds.
New origami structures adapt to over 100 shapes with minimal actuation.
problem Limited shape-morphing capabilities in metamaterials and robotics.
method Hierarchical origami based on polyhedrons, using simple actuation.
result Single structure adapts to over 103 configurations with few actuations.
New origamis found for surfaces with minimal intersections.
problem Finding pairs of curves on surfaces with minimal intersections.
method Using new techniques, constructed exponentially-many to factorial-many pairs of curves.
result Pairs of curves naturally give rise to origamis with minimal intersections.
Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{ä}her manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable po…
Origamis' orbits are non-planar except for a few specific cases.
problem Determining the planarity of origamis' orbits under SL(2,Z) action.
method Analyzing 4-valent graphs from SL(2,Z) action on origamis in H(2).
result Most origamis' orbits are non-planar, with specific exceptions.
Study on mean Euler characteristic of Gorenstein toric contact manifolds.
problem Calculating the mean Euler characteristic of Gorenstein toric contact manifolds.
method Using the relationship between mean Euler characteristic and the normalized volume of the toric diagram, and applying results from Batyrev and Dais.
result Twice the mean Euler characteristic of a Gorenstein toric contact manifold equals the Euler characteristic of any crepant toric symplectic filling.
A flat Klein bottle is visualized using origami.
problem Visualizing a Klein bottle's flatness and topology.
method Curved-crease origami with inelastic film.
result The sculpture illustrates both flatness and non-orientability.
Study on compact toric locally conformally Kähler manifolds, finding specific properties.
problem Characterizing properties of compact toric locally conformally Kähler manifolds.
method Analyzing Kodaira dimension, using specific examples and mappings.
result Kodaira dimension is -∞ for underlying complex manifolds, and specific properties for surfaces and Vaisman manifolds.
New SKT manifolds created using toric geometry.
problem Creating SKT manifolds.
method Using toric geometry and -construction.
result Infinite families of SKT manifolds produced.
Study characterizes toric LCK manifolds, proving conjecture and showing differences from symplectic case.
problem Characterizing compact toric locally conformally Kähler manifolds.
method Proves conjecture about toric LCK manifolds, constructs examples to show differences from symplectic case.
result Proves a conjecture about toric LCK manifolds and shows differences from symplectic case.
The study finds an upper limit for the number of minimal origami pairs on a surface.
problem Counting the minimal origami pairs on a surface of genus g.
method Algorithm to count minimal origami pairs and using Ménage Problem to establish an upper bound.
result Established a new upper bound for the count of minimal origami pairs.
Constructs scalar-flat Kähler metrics on toric symplectic manifolds.
problem Creating scalar-flat Kähler metrics on toric symplectic manifolds.
method Explicit construction and alternative construction with conical singularity.
result Explicit construction of scalar-flat Kähler metrics on toric symplectic manifolds.
A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. T…
Cylindrical contact homology linked to Ehrhart polynomials and Chen-Ruan cohomology.
problem Contact invariants of Q-Gorenstein toric contact manifolds.
method Relationships between cylindrical contact homology and Ehrhart polynomials, Chen-Ruan cohomology.
result Cylindrical contact homology invariants linked to Ehrhart polynomials and Chen-Ruan cohomology.
Uniqueness of Kähler Ricci shrinkers proven on toric orbifolds.
problem Proving uniqueness of Kähler Ricci shrinkers on toric orbifolds.
method Extending results from toric manifolds to toric orbifolds.
result Uniqueness of Kähler Ricci shrinkers on toric orbifolds established.