Ethereum

iarpa.eth

robertghrist.eth

jenkintown.eth

homotopy.eth

At the borders of construction, decomposition, and computation lies the world of spectral sequences. Differentials are the bindings that tie together the pages of the story of algebraic topology.

differentials

Morse theory uses gradient flow -- maximal descent -- to pull homology classes out from a complex. The discrete version chains together combinatorics and dynamics to provide an efficient flow for computing homology.

gradients

Sheaves are algebraic data structures tethered to a base space. The simplest cellular sheaves attach algebraic objects to vertices, edges, and more, while morphing that data across connections. Sheaves encode constraints and enforce consensus.

sheaves

Topology is motivated by the extraction of robust invariants of shape. By lifting data along a line -- be it time or space -- one can call forth those features that persist. The birth, death, and classification of persistent features remains a core component of Topological Data Analysis.

persistence

Cohomology is the algebraic dual of homology, reversing direction, dimension, and implication, forming a rational bridge between homology and homotopy. There is more than what the mirror reflects in this side of homology's split personality.

cohomology

Homologies assemble into algebraic sequences that snake about. The long and short of this exact science is called homological algebra and is invaluable in topological data analysis.

sequences

Homology is the compression of a linear-algebraic signal. Oriented simplices in a vast complex are collapsed down to a homological core, encapsulating holes of various dimensions.

0xd719…f8d6

$0.22

Explore profiles

Company

Learn

Individuals

Businesses

Developers

Support