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Geometry and Topology

Geometry and Topology

The study of shape, space, and continuous deformations, including differential geometry, algebraic topology, geometric analysis, and applications to physics and data analysis

4 papers in this specialization

Paperzilla Papers in Geometry and Topology

An elementary introduction to information geometry

This survey paper provides a concise and self-contained introduction to the core concepts and structures of information geometry, a field that applies differential geometry to information science problems. The paper introduces key structures like conjugate connection manifolds and statistical manifolds, and illustrates their application in areas such as Bayesian hypothesis testing and mixture clustering. It focuses heavily on the mathematical foundations, with less emphasis on practical implementations or specific examples.

Aug 16, 06:07 PM

Advancing mathematics by guiding human intuition with AI

This paper proposes a framework for using machine learning to guide mathematical intuition, demonstrating its application to knot theory and representation theory. In knot theory, the framework led to the discovery of a new relationship between geometric and algebraic invariants, resulting in a novel theorem. In representation theory, it contributed to a conjectured solution to the combinatorial invariance conjecture for symmetric groups, offering a potential resolution to a 40-year-old open problem.

s41586-021-04086-x.pdf

Jul 14, 10:52 AM

THE STRUCTURE OF MEAN EQUICONTINUOUS GROUP ACTIONS

This paper shows that a dynamical system is mean equicontinuous (a relaxed form of isometry) if and only if it's topologically isomorphic to its most regular version. It also connects mean equicontinuity to properties of the system's product and, in certain cases, to its spectral properties.

s11856-022-2292-8.pdf

Jul 14, 10:52 AM

A three-point form factor through five loops

This paper bootstraps the three-point form factor of the chiral part of the stress-tensor supermultiplet in planar N=4 SYM theory to five loops. The authors utilize the recently developed form factor operator product expansion (FFOPE) for boundary data and discover new mathematical structures, including extended-Steinmann-like conditions and multiple-final-entry conditions, simplifying the form factor's structure.

JHEP04(2021)147.pdf

Jul 14, 10:52 AM

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