Research
On-device research index

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.

169,291 papers · 148 categories

Trend · papers per month

count% of corpus
0.3%0.5%0.8%0.1% · Oct 201719922001200920182026
5 results for “walls-and-chambers”
Chamber structure of modular curves X1(N)X_{1}(N)math.AG

The paper studies the geometric structure of modular curves X1(N)X_{1}(N) using meromorphic differentials.

problem Understanding the topological complexity of modular curves X1(N)X_{1}(N).
method Using the walls-and-chambers structure of strata of meromorphic differentials.
result Formulas for the number of chambers and effective means to draw the incidence graph of X1(N)X_{1}(N).
modular curveswalls-and-chambersmeromorphic differentialselliptic curvestopological changes
2017-10-23abs ↗pdf ↗
Isoperiodic foliation of the stratum ΩM1(1,1,−2)Ω\mathcal{M}_1(1,1,-2)math.GT

The paper studies the geometry and topology of a specific foliation on a complex surface.

problem Characterizing the geometry and topology of a specific foliation on a complex surface.
method Analyzes the isoperiodic foliation of the stratum ΩM1(1,1,−2)Ω\mathcal{M}_1(1,1,-2), proving each leaf is a surface of infinite genus.
result Each leaf is a surface of infinite genus homeomorphic to the Loch Ness monster surface.
foliationcomplex surfaceinfinite genusLoch Ness monster surfacesingular Euclidean structure
2023-05-11abs ↗pdf ↗
Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersectionsmath.GR

Study of Coxeter diagrams and Artin-Tits groups, focusing on normalisers and wall intersections.

problem Understanding normalisers of parabolic subgroups in Artin-Tits groups and their connections to Coxeter diagrams.
method Analyzing hyperplane arrangements, Coxeter groups, and wall-and-chamber structures.
result Complexified hyperplane complement is a K(π,1) space for normalisers of parabolic subgroups in finite-type Coxeter diagrams.
Coxeter diagramsArtin-Tits groupsnormalisersparabolic subgroupsTits cone
2025-09-26abs ↗pdf ↗
Spectral networks for polynomial cubic differentialsmath.AG

Study polynomial cubic differentials on Riemann surfaces using spectral networks.

problem Characterize polynomial cubic differentials with saddle connections or critical tripods.
method Introduced spectral core, refined classical core concept, and applied Gaiotto-Moore-Neitzke's algorithm.
result Completely characterized polynomial cubic differentials up to degree 3, including wall-and-chamber structure.
cubic differentialsspectral networksRiemann spheresaddle connectionscritical tripods
2025-07-10abs ↗pdf ↗