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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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10 results for GL2(C[t±1

We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras of rank 22. Our conjecture is motivated by a structure theorem for the degree …

2013-10-26abs ↗pdf ↗

The paper studies rigidity of sphere packings on 3D manifolds with boundary.

problem Rigidity of sphere packings on 3D manifolds with boundary.
method Introduced generalized Thurston's sphere packings and proved their rigidity properties.
result Generalized Thurston's sphere packings are locally determined by combinatorial scalar curvatures and cannot be deformed while keeping combinatorial Ricci curvatures fixed.

Extends rigidity and existence results for discrete conformal structures on surfaces with boundary.

problem Rigidity and existence of discrete conformal structures on surfaces with boundary.
method Axiomatic framework and classification of discrete conformal structures.
result Extends results by Guo-Luo and Guo to a general context.

This paper completes the classification of discrete conformal structures on surfaces.

problem Classifying discrete conformal structures on surfaces.
method Axiomatic approach and study of existing structures.
result Find new classes of discrete conformal structures, including generalized circle packing metrics.

The paper finds hyperbolic metrics on surfaces with boundary using combinatorial curvature flows.

problem Finding hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths.
method Introducing combinatorial Ricci flow and combinatorial Calabi flow for generalized circle packings.
result Proves longtime existence and global convergence of combinatorial curvature flows.

The paper studies rigid sphere packings on 3D manifolds with boundary.

problem Investigating rigid sphere packings on 3D manifolds with boundary.
method Introducing generalized sphere packings, proving rigidity, introducing combinatorial curvature flows.
result Generalized sphere packing metrics are determined by combinatorial scalar curvature.

This paper classifies discrete conformal structures on surfaces with boundary.

problem Classifying discrete conformal structures on surfaces with boundary.
method Axiomatic approach ensuring good geometric structure, classification based on triangulation and axioms.
result Unified and generalized existing discrete conformal structures on surfaces with boundary.

The paper studies curvature flows in Euclidean and hyperbolic spaces, proving smooth convergence to spheres.

problem Analyzing curvature flows in Euclidean and hyperbolic spaces.
method Introduced a class of expanding flows with specific speed functions and proved their longtime existence and smooth convergence.
result The flows converge smoothly to spheres in Euclidean and hyperbolic spaces under certain conditions.