The study constructs AdS manifolds from Gromov-Thurston manifolds.
problem Creating hyperbolic and anti-de Sitter structures from Gromov-Thurston manifolds.
method Explicit correspondence between quasifuchsian AdS manifolds and compact quotients of Ø(2d,2)/U(d,1).
result Existence of quasifuchsian AdS manifolds and hyperbolic ends with specified boundary.
New method constructs AdS 3-manifolds and applies to Higgs bundles and minimal immersions.
problem Understanding AdS 3-manifolds and their connections to Higgs bundles and minimal immersions.
method Developed a new construction method for AdS structures.
result Recovered Tholozan's formula for AdS 3-manifold volumes and characterized representations for minimal immersions.
Proves existence of AdS manifold with prescribed metrics on boundary.
problem Prescribing metrics on the boundary of AdS 3-manifolds.
method Using duality between convex space-like surfaces in AdS₃, proves existence of AdS manifold with prescribed metrics.
result Existence of AdS manifold with prescribed metrics on boundary.
A new method for precise user targeting in advertising using hyperbolic manifold learning.
problem Improving user satisfaction in targeted advertising by overcoming skepticism and spam perception.
method Proposes a Multi-Manifold Learning framework to learn hierarchical user and ad representations in the hyperbolic space.
result Demonstrates improved performance in user targeting and prediction accuracy on both public datasets and a large-scale commercial system.
Inverse curvature flows in AdS-Schwarzschild manifold converge to a sphere.
problem Understanding the behavior of hypersurfaces in AdS-Schwarzschild geometry.
method Non-parametric inverse curvature flows with 1-homogeneous curvature function.
result Principle curvatures converge to 1 exponentially fast.
Topological twist of gauge theories mapped to AdS/CFT.
problem Mapping topological gauge theories to holographic duals.
method Asymptotically locally hyperbolic solutions to gauged supergravity.
result Partition function independence under AdS/CFT.
The study explores Sasaki-Einstein manifolds and their connections to field theories and AdS/CFT.
problem Understanding the geometric and algebraic properties of Sasaki-Einstein manifolds and their dual field theories.
method Algebraic and geometric methods to analyze Sasaki-Einstein manifolds and associated singularities.
result Proposed a conjecture to simplify the check of K stability for finding more SE metrics.
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph Γ. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π on time-like singular segments). We construct examples of such manifolds, d…
Landmark AD improves AD's efficiency without sacrificing performance.
problem Computational burden in diffusion-based sensor fusion.
method Inspired by landmark diffusion, proposes Landmark AD.
result Landmark AD offers superior computational efficiency.
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient …
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path i…
Study of supersymmetric AdS solutions using fibred GK geometries.
problem Understanding flux quantization and supersymmetric Killing vectors in AdS solutions.
method Analysis of GK geometries that fibre over Kähler bases, using master volume and global data.
result Quantum mechanical and SCFT central charges and entropy can be computed without explicit geometry.
We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we…
We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.
B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators C(S), which are nonnegative in a suitable sense, to every $Ad_{SO(n,\C)}$ invariant subset $S \subset {\bf so}(n,\C)$. For curvature operators of a Kähler manifold of complex dimension n, one considers $Ad_{GL(n,\…
Study numerically flat bundles on Fujiki manifolds using algebraic groups.
problem Characterize numerically flat principal bundles on Fujiki manifolds.
method Analyzes holomorphic principal bundles and their quotient structures, proving equivalence of conditions involving numerically flat ad bundles and nef line bundles.
result Establishes equivalence among numerically flat ad bundles, nef line bundles, and degree inequalities for reductions of structure groups.
Study shows how any group can be fundamental of a non-orientable 4-manifold with exotic structure.
problem Realizing any finitely presented group as the fundamental group of a non-orientable 4-manifold with exotic structure.
method Performing a Gluck twist to obtain an exotic smooth structure, and using 2-covers to stabilize the structure.
result Any finitely presented group can be realized as the fundamental group of a non-orientable 4-manifold with exotic structure.
This paper contains a classification of smooth Kaluza--Klein reductions (by one-parameter subgroups) of the maximally supersymmetric anti de Sitter backgrounds of supergravity theories. We present a classification of one-parameter subgroups of isometries of anti de Sitter spaces, discuss the causal properties of their …
Study on linear independence of Poincaré series for anti-de Sitter 3-manifolds.
problem Linear independence of generalized Poincaré series for anti-de Sitter 3-manifolds.
method Analysis of eigenfunctions and Laplacian on anti-de Sitter 3-manifolds.
result Unbounded multiplicities of eigenvalues for L2-eigenfunctions and stable L2-eigenvalues. The paper proves positive energy-momentum theorems for charged AdS initial data sets.
problem Proving positive energy-momentum theorems for charged asymptotically AdS initial data sets.
method Introducing a charged energy-momentum functional and establishing positive theorems under a dominant energy condition.
result The charged energy-momentum functional is non-negative on a natural real cone.
The study finds invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.
problem Existence of invariant Einstein metrics on complex Stiefel manifolds and special unitary groups.
method Decomposing Lie algebras and tangent spaces, parametrizing scalar products, and computing Ricci tensors for invariant metrics.
result Existence of invariant Einstein metrics on specific special unitary groups and complex Stiefel manifolds.
Study of black hole entropy from 4d theories on hyperbolic manifolds.
problem Determining the entropy of magnetically charged black holes in AdS5. method Analytic torsions twisted by flat connections on hyperbolic 3-manifolds, perturbative expansion of index.
result The leading part of the index matches the Bekenstein-Hawking entropy of a magnetically charged black hole.
This is an expository paper describing the geometry of certain Sasakian-Einstein manifolds. Such manifolds have recently become of interest due to Maldacena's AdS/CFT conjecture. They describe near-horizon geometries of branes at conical singularities.
We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result is that the space of ``globally hyperbolic'' AdS manifolds with ``parti…
Study on Killing vector fields with constant length on Riemannian manifolds.
problem Properties of Killing vector fields of constant length on Riemannian manifolds.
method Analysis of the linear operator ad(X) and its spectrum.
result The linear operator ad(X) has a pure imaginary spectrum.
Study of Poincare-Lovelock metrics on conformally compact manifolds.
problem Understanding Poincare-Lovelock metrics in conformally compact geometry.
method Fefferman-Graham expansion and Lovelock equation analysis.
result Existence of fillings for conformal classes near round sphere.
Researchers prove unique foliation of AdS space-time with constant Gauss curvature surfaces.
problem Proving unique foliation of AdS space-time with constant Gauss curvature surfaces.
method Analyzing convex globally hyperbolic maximal AdS 3-dimensional spaces with particles.
result A unique foliation by constant Gauss curvature surfaces in the complement of the convex core.
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph Γ. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π on time-like singular segments). We construct examples of such manifolds, d…
Kepler metrics linked to gravity and string theory.
problem Kepler metrics and their geometric properties.
method Sasakian and Hessian geometry approaches.
result Established connection between gravity and string theory.
Let S be a closed surface of genus at least 2, and consider two measured geodesic laminations that fill S. Right earthquakes along these laminations are diffeomorphisms of the Teichmüller space of S. We prove that the composition of these earthquakes has a fixed point in the Teichmüller space. Another way to state this…
The study counts periodic orbits on smooth manifolds, adding ghost orbits for completeness.
problem Counting periodic orbits of vector fields on smooth closed manifolds.
method Enlarging the space of orbits to include ghost orbits, defining weight functions, and showing constancy under deformation.
result The weight function remains constant as the vector field moves and Γ deforms. We prove that an (n+1)-dimensional spin static vacuum with negative cosmological constant whose null infinity has a boundary admitting a non-trivial Killing spinor field is the AdS spacetime. As a consequence, we generalize previous uniqueness results by X. Wang \cite{Wa2} and by Chru{ś}ciel-Herzlich \cite{CH} and in…
Study on hyperbolic manifolds and their boundary data, focusing on volume functions.
problem Determining the hyperbolic metric from boundary data of convex co-compact hyperbolic manifolds.
method Analysis of volume functions and their relation to boundary data, using first variations.
result New connections with physics and probability theory, with open questions remaining.
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove the existence of isoperimetric regions in a larger space obtained by adding finitely many limit manifolds at infinity. As one of many possible applications, we extend properties of the isoperimetric profile from compact manifolds to…
The paper connects G2-manifolds to Coulomb and Higgs phases of gauge theories.
problem Exploring the physical interpretation of special singularities in G2-holonomy manifolds. method Analyzing desingularizations of orbifold singularities and relating them to gauge theories.
result Shows an isomorphism between moduli spaces of Ricci flat metrics and flat ADE-connections.
We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifo…
3D topological order linked to Seifert manifolds and gauge groups.
problem Classifying 3D topological orders using Seifert manifolds and gauge groups.
method Correspondence between topological order, Seifert manifolds, and ADE gauge groups.
result Construction of modular fusion categories from Seifert manifolds and gauge groups.
Perceptual ad-blocking is vulnerable to attacks, creating new security risks.
problem Vulnerability of perceptual ad-blocking to attacks and new security risks.
method Analysis and creation of adversarial examples to bypass perceptual ad-blocking.
result Perceptual ad-blocking can be bypassed using adversarial examples, introducing new security risks.
The interior Kasparov product formula is extended for foliated ρ-classes on Riemannian bundles.
problem Extending the Kasparov product formula for foliated ρ-classes.
method Construction of asymptotic morphisms and adiabatic deformation groupoids.
result Interior Kasparov product formula for foliated ρ-classes on Riemannian bundles.
The paper tests a conjecture about mass and scalar curvature in AdS/CFT.
problem Proving a conjecture about mass and scalar curvature in asymptotically Poincaré-Einstein metrics.
method Assuming the conjecture is true, proving a corollary about scalar curvature rigidity.
result The minimum mass metric must be static Einstein, leading to static uniqueness.
A new framework for personalized ad retrieval in e-commerce search.
problem Difficulty in measuring ads retrieved using multiple signals (e.g. user profiles, clicks).
method Employing historical click data to initialize a hierarchical network representing signals, keys, and ads. Training a model to learn weights of edges and selecting the best edges.
result Framework achieves good performance, improving RPM/CTR.
Study end sum for surfaces and prove uniqueness results.
problem Uniqueness of end sum for surfaces and related manifolds.
method Analyzing end sum and adding a 1-handle at infinity for surfaces.
result The end sum of two surfaces with compact boundary is uniquely determined by the chosen ends.
The paper introduces a new loss function to prevent overfitting in semi-supervised graph networks.
problem Overfitting in semi-supervised graph networks trained with cross-entropy loss.
method Proposes an unsupervised manifold smoothness loss to regularize the graph convolutional networks.
result Adding the proposed loss consistently improves performance of graph networks.
The paper examines stability of Minkowski inequalities in warped product spaces.
problem Stability of Minkowski-type inequalities for hypersurfaces in warped product spaces.
method Established a stability estimate for the norm of the traceless second fundamental form.
result Proved stability of Minkowski inequalities in specific warped product examples.
This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of k planar landmarks (k>2)-modulo translation, scaling a…
Let π: V \rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\circ_{V},e_{V},g_{V}). Using a connection D on the bundle V and a morphism α: V \rightarrow TM, we construct an almost Froben…
The paper introduces a differentially private method for optimization on Riemannian manifolds.
problem Differential privacy in optimization constrained to Riemannian manifolds.
method Adding Gaussian noise to the Riemannian gradient on the tangent space, with privacy and utility guarantees.
result Privacy and utility guarantees for differentially private Riemannian optimization.
We establish various stability results for symplectic surfaces in symplectic 4−manifolds with b+=1. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic 4−manifolds with κ=−∞. This involve…