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arXiv research

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.

168,695 papers · 148 categories

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9 results for “Goncharov-Shen”

Unbounded

\mathfrak{sl}_3

-laminations around puncturesmath.RT

Study unbounded $\mathfrak{sl}_3$ -laminations around punctures.

problem Classify and understand structures of

\mathfrak{sl}_3

-laminations at punctures.

method Relate to root data, classify signed webs, describe tropicalization, clarify relationships with other approaches.

result Clarify the relationship between

\mathfrak{sl}_3

-laminations and other approaches.

$\mathfrak{sl}_3$-laminations punctures root data tropicalization Goncharov-Shen

2024-04-28abs ↗pdf ↗

Wilson lines and their Laurent positivitymath.RT

Wilson lines generate positive Laurent polynomials in decorated triangulations.

problem Wilson lines and their coefficients in function algebras.

method Study of Wilson lines on marked surfaces and their matrix coefficients in function algebras.

result Matrix coefficients of Wilson lines give Laurent polynomials with positive integral coefficients.

Wilson lines Laurent polynomials function algebras decorated triangulations positive coefficients

2020-11-29abs ↗pdf ↗

Train track combinatorics and cluster algebrasmath.GT

Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.

problem Understanding pseudo-Anosov mapping classes on surfaces.

method Using Goncharov--Shen's potential function, the paper translates train track concepts into cluster algebra language.

result Proves sign stability of general pseudo-Anosov mapping classes.

train tracks pseudo-Anosov mapping classes cluster algebras sign stability measured foliations

2023-03-06abs ↗pdf ↗

SU(3)-skein algebras and webs on surfacesmath.GT

Developed a theory for $SU_3$ -skein algebras on surfaces, proving finitely generated property.

problem Quantization of

SL(3)

-character varieties of surfaces.

method Theory of canonical forms of webs, ideal triangulations, and crossbar moves.

result Reduced

SU_3

-skein algebra of any surface of finite type is finitely generated.

SU(3)-skein algebras webs on surfaces character varieties finite generation canonical forms

2020-02-17abs ↗pdf ↗

McShane identities for Higher Teichmüller theory and the Goncharov-Shen potentialmath.GT

We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen which generalize the notion of horocycle lengths. In particular, we obtain McShane-type identities for finite-area cusped conve…

2019-01-07abs ↗pdf ↗

Unbounded

\mathfrak{sl}_3

-laminations and their shear coordinatesmath.GT

Geometric model of unbounded sl3 laminations with tropical coordinates.

problem Modeling unbounded laminations in cluster varieties.

method Introducing tropical cluster coordinates and geometric gluing procedures.

result Established a geometric gluing procedure for unbounded sl3 laminations.

sl3 laminations cluster varieties tropical coordinates geometric gluing shear coordinates

2022-04-19abs ↗pdf ↗

Teichmüller and lamination spaces with pinningsmath.GT

Spaces of positive and tropical points described as Teichmüller and lamination spaces with pinnings.

problem Describing spaces of positive and tropical points in moduli space with pinnings.

method Topological description of Teichmüller and lamination spaces with pinnings.

result Formulae relating functions on Teichmüller space with pinnings and topological description of tropicalized amalgamation map.

Teichmüller spaces lamination spaces pinnings moduli space Fock-Goncharov duality

2022-12-30abs ↗pdf ↗

Tropical Fock-Goncharov coordinates for

\mathrm{SL}_3

-webs on surfaces II: naturalitymath.GT

Natural coordinates for SL3-webs on surfaces are shown to be consistent under triangulation changes.

problem Natural coordinates for SL3-webs on surfaces.

method Showed natural coordinates are consistent under triangulation changes using cluster transformations.

result Natural coordinates for SL3-webs on surfaces are consistent under triangulation changes.

SL3-webs tropical coordinates natural coordinates cluster transformations surface triangulations

2020-12-28abs ↗pdf ↗

WKB asymptotics of Stokes matrices, spectral curves and rhombus inequalitiesmath-ph

Study of WKB asymptotics of Stokes matrices and spectral curves, proving rhombus inequalities.

problem Analyzing WKB asymptotics of Stokes matrices and spectral curves.

method Using spectral network theory, Poisson geometry, and cluster structures.

result Real parts of leading WKB exponents satisfy rhombus inequalities.

WKB asymptotics Stokes matrices spectral curves rhombus inequalities cluster structures

2024-03-26abs ↗pdf ↗