Algebraic topology: The study of topological spaces with methods from abstract algebra, emphasising the transformation of geometric problems into algebraic ones. Homotopy theory: ...

Fittingly, the group structure of homology was discovered in the 1920s by Emmy Noether, a pioneer of the study of groups and other algebraic structures. Thanks to Noether’s observation, mathematicians ...

Algebraic topology is quite abstract but its results are easy to understand. If two systems' geometric objects are qualitatively similar, they contain the same number of holes.

Lights, Camera and Algebraic Topology! Imagine a lazy weekend night winding down, as so many do at Harvard, with a trip to the local video. By Simon W. Vozick-levinson.

January 06, 2016 Penn professor, leader in topology, changing the face of math education Robert Ghrist, a Penn Integrates Learning Professor, wants to bring algebraic topology to the masses ...

He told family members algebraic topology is “math at its purest form,” an area, he said, where math verges on poetry. U. of C. colleague Peter May said in an email that, ...

Hess, a researcher at the Swiss Federal Institute of Technology, is one of the world’s leading thinkers in the field of algebraic topology—in super simplified terms, the mathematics of rubbery ...

This will be a first course on algebraic topology, following on from the introduction to topology given in the Level 3 course Metric spaces. Topology studies the shape of space, with examples such as ...

Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group theory, and geometric topology. Page updated February 18, 2025 . ... Low-Dimensional ...

These are the types of questions arising from the growth of big data – and algebraic topology provides some answers. Spheres, cubes, look the same to me. Phil Shirley, CC BY-NC-ND ...