Penn-led researchers have shown for the first time that multiple, information-carrying light signals can be safely guided through chip-based, reconfigurable networks using topology, the esoteric ...
To many in the United States, advanced forms of mathematics are a terrifying maze of numbers, symbols, graphs, and hypotheticals that render our world more complex than simple observations would ...
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Why knots come undone in 4D, but 2D surfaces can still be knotted
Tie a trefoil knot in a piece of string, seal the ends together, and try to wiggle it free without cutting. In three-dimensional space, the knot holds firm. Add a fourth spatial dimension, however, ...
When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Professor Pekka Pankka. Geometry, Algebra, and Topology are pure mathematics and essential ...
The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group ...
Dr. Das has taught a broad range of courses, from Quantitative Skills and Mathematical Reasoning to graduate-level Topology and Analysis. He has mentored over 25 capstone research projects and has ...
Endperiodic maps, splitting sequences, and branched surfaces. Michael Landry and Chi Cheuk Tsang. To appear in Geometry and Topology. 144 pages. A polynomial invariant for veering triangulations.
The mathematics hidden in materials keeps getting more exotic. Topological states of matter — which derive exotic properties from their electrons’ ‘knotty’ quantum states — have shot from rare ...
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