Paper proves Gromov's cube inequality in all dimensions.
problem Proving Gromov's cube inequality on scalar curvature in all dimensions.
method Used Dirac operator method to prove cube inequality with optimal constant.
result Proved cube inequality in all dimensions with optimal constant.
Proposes a method to align Hawkes processes across different event spaces.
problem Aligning Hawkes processes in multiple event spaces.
method Fused Gromov-Wasserstein alignment for Hawkes processes.
result The method effectively aligns Hawkes processes and their event types.
A scalable method for graph partitioning and matching using Gromov-Wasserstein discrepancy.
problem Graph partitioning and matching for large-scale graphs.
method Recursive K-partition mechanism with proximal gradient algorithm. result Achieves a trade-off between accuracy and efficiency.
A method for learning embeddings from multi-view data using Gromov-Wasserstein.
problem Challenges in learning low-dimensional representations from multi-view relational data with differing geometries.
method Bary-GWMDS and Mean-GWMDS-C, Gromov-Wasserstein-based methods operating on distance matrices.
result Stable and geometrically meaningful embeddings learned from synthetic and real-world datasets.
The paper extends Gromov's non-squeezing theorem to deformed symplectic forms.
problem Extending Gromov's non-squeezing theorem to deformed symplectic forms.
method Trap idea for holomorphic curves analogous to dynamical systems.
result The classical Gromov argument breaks down for deformed forms.
Method learns graphons from graphs via Gromov-Wasserstein barycenters.
problem Learning nonparametric graph models from finite graphs.
method Approximate graphons with step functions, use Gromov-Wasserstein distance, learn barycenters.
result Proposed method outperforms state-of-the-art on synthetic and real-world data.
New proof shows no Hölder embeddings into Heisenberg group.
problem Non-existence of Hölder embeddings into Heisenberg group.
method Developed a new elementary proof method.
result Generalization of Gromov's theorem proven.
Study uses equivariant topology to measure distances between G metric spaces.
problem Measuring distances between G metric spaces.
method Equivariant topology methods to derive lower bounds.
result Sharp bounds on Gromov Hausdorff distance between spheres.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
New method uses cohomology to quantify molecular similarity.
problem Quantifying structural dissimilarity in molecular data.
method Gromov-Hausdorff ultrametric based on simplicial complexes and cohomology.
result Demonstrates effectiveness in clustering organic-inorganic halide perovskite structures.
Extends subspace detour method to Gromov-Wasserstein problem.
problem Matching shapes using Gromov-Wasserstein distance.
method Project measures onto a subspace, then compute optimal transport plan.
result Connections with Knothe-Rosenblatt rearrangement.
Compactness theorem for manifolds with boundary proved.
problem Proving convergence of manifolds with boundary.
method Reduction to Hamilton's compactness theorem for manifolds without boundary.
result Cheeger-Gromov convergence for a subsequence of manifolds with bounded geometry.
Proof of Gromov's conjecture in 3D simplifies existing methods.
problem Gromov's dihedral rigidity conjecture on scalar curvature in 3D.
method Self-contained proof avoiding technical complications, shorter and more accessible than general case.
result Simplified proof of Gromov's conjecture in 3D.
Proposes a novel framework for graph matching and node embedding.
problem Graph matching and node embedding in real-world networks.
method Gromov-Wasserstein discrepancy for graph dissimilarity, optimal transport for correspondence, structural regularizers for learning.
result Superior performance in graph matching compared to alternative approaches.
Explains Gromov's and Rumin's work on Carnot manifolds.
problem Hölder equivalence problem for Carnot manifolds
method PDE techniques and Rumin's complex
result Both methods yield similar conclusions for the H{ö}lder equivalence problem
A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.
problem Lack of principled uncertainty quantification for graph-valued supervised prediction.
method Proposes a conformal prediction framework using Z-Gromov-Wasserstein distances for graph-valued outputs.
result Provides distribution-free coverage guarantees for graph-valued outputs.
We give here some extensions of Gromov's and Polterovich's theorems on $\karea$ of CPn, particularly in the symplectic and Hamiltonian context. Our main methods involve Gromov-Witten theory, and some connections with Bott periodicity, and loop groups. The argument is closely connected with study of jump…
We make an estimation of the value of the Gromov norm of the Cartesian product of two surfaces. Our method uses a connection between these norms and the minimal size of triangulations of the products of two polygons. This allows us to prove that the Gromov norm of this product is between 32 and 52 when both factors hav…
The paper proves Gromov hyperbolicity of certain metrics using isoperimetric inequalities.
problem Investigating Gromov hyperbolicity of specific metrics.
method Using isoperimetric inequalities to characterize Gromov hyperbolicity.
result Characterization of domains where these metrics are Gromov hyperbolic.
Develops a private synthetic graph generator using Gromov-Wasserstein distance.
problem Creating private synthetic networks for complex data.
method Random connection model, fused Gromov-Wasserstein distance, differential privacy.
result Effective algorithm for generating private synthetic graphs with theoretical guarantees.
New method learns disentangled representations using Gromov-Monge maps.
problem Learning disentangled representations from unlabelled data.
method Introduces a novel approach based on Gromov-Monge maps to preserve geometric features while aligning data distributions.
result Demonstrates effectiveness on four benchmarks, outperforming other methods.
Proof of Gromov's theorem on convex polytopes with acute angles.
problem Gromov's conjecture on extremal scalar curvature of convex polytopes.
method Smoothing construction using Dirac operator techniques.
result Detailed proof of Gromov's theorem.
Unified method to calculate Gromov norm for Kähler classes of bounded symmetric domains.
problem Calculating the Gromov norm of Kähler classes for all bounded symmetric domains.
method Combination of ideas from Domin-Toledo and Toledo, aided by the Polydisc Theorem.
result Unified and simplified calculation of Gromov norm for all bounded symmetric domains.
New theorem using Ricci flow for Gromov almost flat manifolds.
problem Conditions for Gromov almost flat manifolds.
method Employing Ricci flow to derive a new theorem.
result New theorem with weaker condition than Gromov--Ruh Theorem.
Proves Gromov's conjecture on metric operators.
problem Non-free isometric immersions and metric operators.
method Proof of a conjecture.
result Infinitesimal invertibility of metric inducing operators proven.
Two tropical gluing formulas help calculate Gromov-Witten invariants.
problem Calculating Gromov-Witten invariants of symplectic manifolds.
method Tropical geometry applied to exploded manifolds.
result Generalizes existing formulas for Gromov-Witten invariants.
Potential theory extended to Gromov hyperbolic spaces.
problem Extending potential theory to a new class of spaces.
method Unified framework for Gromov hyperbolic metric measure spaces.
result Boundary Harnack inequalities and complete classification of positive harmonic functions.
Unified framework for DR and clustering using Gromov-Wasserstein.
problem Capturing structure in high-dimensional datasets.
method Distributional reduction framework using Gromov-Wasserstein.
result Unified approach recovers DR and clustering as special cases.
The study proves Gromov hyperbolicity for certain complex domains.
problem Characterizing Gromov hyperbolicity for complex domains.
method Analyzing domains in C2 with finite d'Angelo type and using automorphisms. result Domains in C2 with finite d'Angelo type are Gromov hyperbolic. It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper we introduce the cl…
Connectivity proven in large rank Gromov boundary of free factor complex.
problem Connectivity of Gromov boundary in large rank free factor complex.
method Analyzing Gromov boundary and free factor complex properties.
result Gromov boundary is path connected and locally path connected in large rank.
New proof for Gromov's theorem on almost flat manifolds.
problem Proving Gromov's theorem on almost flat manifolds.
method Inductive proof on dimension.
result New proof for Gromov's theorem.
The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.
problem Stability in compact finite dimensional Alexandrov spaces.
method Equivariant Gromov--Hausdorff convergence and almost commutative diagrams.
result Stability result in compact finite dimensional Alexandrov spaces.
Gromov boundary described for ray graph action.
problem Understanding the boundary of ray graph.
method Description of Gromov boundary in terms of cliques of long rays.
result Gromov boundary is homeomorphic to a subset of the circle.
Note on the computational complexity of Gromov-Wasserstein distance.
problem Computational difficulty of Gromov-Wasserstein distance.
method Analysis of the optimization problem structure and providing explicit examples.
result Gromov-Wasserstein distance optimization problem is non-convex quadratic.
A new method efficiently approximates Gromov-Wasserstein distance.
problem High computational complexity of Gromov-Wasserstein distance.
method Importance sparsification method to construct a sparse coupling matrix.
result Efficient approximation of GW distance with reduced complexity.
GWIB improves counterfactual regression by balancing latent distributions and reducing selection bias.
problem Selection bias between control and treatment groups negatively impacts counterfactual regression performance.
method GWIB uses Gromov-Wasserstein information bottleneck to maximize mutual information between covariates and outcomes while penalizing kernelized mutual information between latent representations and covariates.
result GWIB consistently outperforms state-of-the-art CFR methods in ITE estimation tasks.
In 1969 M. Gromov in his PhD thesis greatly generalized Smale-Hirsch-Phillips immersion-submersion theory by proving what is now called the h-principle for invariant open differential relations over open manifolds. Gromov extracted the original geometric idea of Smale and put it to work in the maximal possible generali…
Continuity method yields Kähler-Einstein metric on elliptic surfaces.
problem Proving convergence of continuity method on elliptic Kähler surfaces.
method Continuity method applied to Kähler metrics on elliptic surfaces.
result Continuity method converges to Kähler-Einstein metric.
Develop criteria to distinguish Gromov-Thurston manifolds using algebraic Dehn fillings.
problem Distinguishing homotopy types of Gromov-Thurston manifolds
method Using virtual Dehn fillings of relatively hyperbolic groups
result Criteria to distinguish homotopy types
Compact sequences of manifolds with boundary converge smoothly under conformal transformations.
problem Compactness of sequences of manifolds with boundary under conformal transformations.
method Use of stable elliptic estimates and the 'flatzoomer' method.
result Smooth Cheeger-Gromov convergence of sequences of manifolds with boundary under conformal transformations.
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
Extends Gromov's theorem with amenable covers.
problem Gromov's Vanishing Theorem limitations.
method Gromov's multicomplex theory, relative bounded cohomology.
result Relative version of Gromov's Vanishing Theorem.
Differentiable optimization bridges arbitrary metrics to tree metrics.
problem Designing algorithms to convert arbitrary metrics to tree metrics with guarantees.
method DeltaZero framework, leveraging differentiable Gromov hyperbolicity.
result DeltaZero consistently achieves state-of-the-art distortion on synthetic and real-world datasets.
Boundary rigidity defined for hyperbolic spaces, tied to geometric properties.
problem Understanding boundary rigidity in Gromov hyperbolic spaces.
method Analyzing properties of Gromov hyperbolic spaces and their boundaries.
result Boundary rigidity is equivalent to positive Cheeger isoperimetric constant and non-amenability.
Study on non-Gromov hyperbolic tube domains and their geometric properties.
problem Characterizing non-Gromov hyperbolic tube domains with convex bases.
method Provided a criterion for non-Gromov hyperbolicity, studied Hilbert metric, and continuity properties of complex geodesics.
result Similarity of geometry of tube domains and convex domains, connections between metrics.
An older paper by Edwards introduced the Gromov-Hausdorff distance.
problem Determining the first inventor of the Gromov-Hausdorff distance.
method Comparing metric spaces through isometric embeddings and measuring Hausdorff distance.
result David Edwards published the Gromov-Hausdorff distance 6 years before M. Gromov.
Extends Gromov's optimal systolic inequality to manifolds with specific cohomology properties.
problem Finding optimal systolic inequalities for manifolds with complex cohomology structures.
method Extends Gromov's inequality to manifolds with fundamental cohomology classes as cup products of 2-dimensional classes.
result Provides an optimal systolic inequality for a new class of manifolds.