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Research Paper#Geometry, Number Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:40

Rational Angle Bisection and Incenters in Higher Dimensions

Published:Dec 31, 2025 06:14
1 min read
ArXiv

Analysis

This paper extends the classic rational angle bisection problem to higher dimensions and explores the rationality of incenters of simplices. It provides characterizations for when angle bisectors and incenters are rational, offering insights into geometric properties over fields. The generalization of the negative Pell's equation is a notable contribution.
Reference

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

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Research Paper#Knot Theory, Conformal Field Theory, Gauge Theory🔬 ResearchAnalyzed: Jan 3, 2026 19:12

Torus Knots, Minimal Models, and VOA Characters

Published:Dec 29, 2025 00:16
1 min read
ArXiv

Analysis

This paper revisits the connection between torus knots and Virasoro minimal models, extending previous work by leveraging the 3D-3D correspondence and bulk-boundary correspondence. It provides a new framework for understanding and calculating characters of rational VOAs, offering a systematic approach to derive these characters from knot complement data. The work's significance lies in bridging different areas of physics and mathematics, specifically knot theory, conformal field theory, and gauge theory, to provide new insights and computational tools.
Reference

“The paper provides new Nahm-sum-like expressions for the characters of Virasoro minimal models and other related rational conformal field theories.”

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