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In mathematics, a geometric algebra is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division and addition of objects of different dimensions.
William Kingdon Clifford was a British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression mind-stuff.
David Orlin Hestenes is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.
Sir Erik Christopher Zeeman FRS, was a British mathematician, known for his work in geometric topology and singularity theory.
Michael Paul Fourman is Professor of Computer Systems at the University of Edinburgh in Scotland, UK, and was Head of the School of Informatics from 2001 to 2009.
Andrew John Casson FRS is a mathematician, studying geometric topology. Casson is the Philip Schuyler Beebe Professor of Mathematics at Yale University.
Joan Sylvia Lyttle Birman is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.
Dame Frances Clare Kirwan, is a British mathematician, currently Savilian Professor of Geometry at the University of Oxford. Her fields of specialisation are algebraic and symplectic geometry.
In the study of geometric algebras, a k-blade or a simple k-vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically, a k-blade is a k-vector that can be expressed as the exterior product of 1-vectors, and is of gradek.
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
Chris J. L. Doran is a physicist, Director of Studies in Natural Sciences for Sidney Sussex College, Cambridge. He founded Geomerics, and is its Chief Operating Officer.
Conformal geometric algebra (CGA) is the geometric algebra constructed over the resultant space of a map from points in an n-dimensional base space Rp,q to null vectors in Rp+1,q+1. This allows operations on the base space, including reflections, rotations and translations to be represented using versors of the geometric algebra; and it is found that points, lines, planes, circles and spheres gain particularly natural and computationally amenable representations.
In geometric algebra, the outermorphism of a linear function between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior algebras whose restriction to the vector spaces is the original function.
Stephen Gull is a British physicist based at St John's College, Cambridge credited, together with Anthony N. Lasenby, Joan Lasenby and Chris J. L. Doran, with raising the interest of the physics community to the mathematical language and methods of geometric algebra and geometric calculus. These have been rediscovered and refined by David Hestenes, who built on the fundamental work of William Kingdon Clifford and Hermann Grassmann. In 1998, together with Lasenby and Doran, he proposed gauge theory gravity.
Judy Leavitt Walker is an American mathematician. She is the Aaron Douglas Professor of Mathematics at the University of Nebraska–Lincoln, where she chaired the mathematics department from 2012 through 2016 and currently serves as the Associate Vice Chancellor for Faculty Affairs. Her research is in the area of algebraic coding theory.
Andrew Alexander Ranicki was a British mathematician who worked on algebraic topology. He was a professor of mathematics at the University of Edinburgh.
Elaine Chew is an operations researcher and pianist focused on the study of musical structures as they apply to musical performance, composition and cognition, the analysis of electrocardiographic traces of arrhythmia, and digital therapeutics. She is currently Professor of Engineering at King's College London, where she is jointly appointed in the Department of Engineering and the Department of Cardiovascular Imaging in the School of Biomedical Engineering & Imaging Sciences.
Greta Cvetanova Panova is a Bulgarian-American mathematician. She is a professor of mathematics and Gabilan Distinguished Professor in Science and Engineering at the University of Southern California in Los Angeles. Her research interests include combinatorics, probability and theoretical computer science.
Karin Melnick is a mathematician and Professor at the University of Luxembourg. She specializes in differential geometry and was awarded the 2020-2021 Joan and Joseph Birman Fellowship for Women Scholars by the American Mathematical Society.
Anne-Sophie Kaloghiros is a mathematics researcher in algebraic geometry and reader in Mathematics at Brunel University London. Kaloghiros was awarded the London Mathematical Society (LMS) Emmy Noether Fellowship in 2020.
References
- 1 2 3 "Professor Joan Lasenby", Profiles, Cambridge Department of Engineering, 26 November 2013, retrieved 2025-01-19
- ↑ Lasenby, Joan (Spring 2008), "In at the beginning", The Fountain, vol. 6, pp. 4–5, retrieved 2025-01-19– via Issuu.com