Sentences with phrase «algebraic topology»
Algebraic topology is a branch of mathematics that studies how shapes and spaces can be compared and classified using algebraic methods. It uses algebraic tools, such as groups and equations, to examine the properties that remain the same even when shapes are stretched, twisted, or bent. This field helps mathematicians understand the structure and properties of spaces by translating geometric problems into algebraic language. Full definition
I'm a third year math student in the PhD program at the CUNY Graduate Center, and my research interests lie in algebraic topology with applications to quantum physics.
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Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.
Perhaps functoriality had to await the further maturation of cross-disciplinary fields such as algebraic topology and algebraic geometry, but in light of Whitehead's eccentric tastes, we doubt that fifty years would have made much difference.
This is where algebraic topology comes in: a branch of mathematics that can describe systems with any number of dimensions.
The mathematicians who brought algebraic topology to the study of brain networks in the Blue Brain Project were Kathryn Hess from EPFL and Ran Levi from Aberdeen University.
Their analysis of these cliques, using methods from algebraic topology, revealed an organized geometric structure.
«We have adopted approaches from the field of algebraic topology that previously had been used primarily in the domain of pure mathematics and have applied them to experimental data on the activity of place cells — specialized neurons in the part of the brain called the hippocampus that sense the position of an animal in its environment,» said Curto.
In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance.
He has over 60 research papers in mathematics, specializing in algebraic topology.
The work of these men led directly to the key mathematical structures, methods, and programs that have persisted through this century: groups, rings, modules, and field extensions; algebraic and analytic number theory; algebraic geometry; algebraic topology and qualitative analysis of dynamical systems; Hilbert's twenty - three problems.
«Algebraic topology is like a telescope and microscope at the same time.