A first introduction to Clifford algebras
William Kingdon Clifford (1845-78) died of tuberculosis when he was still young: he was a professor of Mathematic and Mechanics at University College, London. His work on “geometrical algebra” foreshadowed the theory of general relativity. Almost a century later David Hestenes used Clifford’s ideas to develop “space-time algebra”: these ideas are still being actively developed as a basis for physics.
The talk is going to start with a very basic mathematical first introduction to “geometrical algebra”. Applications to physics are reached by considering Clifford’s geometrical algebras in the context of tangent categories and (hopefully) I will end on some remarks in this direction.