| Speaker: Kenneth Johnson Affiliation: Pennsylvania State University Time: 12:00 Thursday, 29 March, 2018 Location: 303-257 |
| It is not well-known that Frobenius invented group character theory for nonabelian groups in order to answer a question put to him by Dedekind: How does the group determinant factorise? The group matrix of a group of order n is obtained from its Cayley table by switching each column corresponding to an element with that corresponding to its inverse, and then replacing each element by a variable attached to the element. The group determinant is the determinant of this matrix. It is a polynomial in n variables of degree n. I will give an account of Frobenius' work and explain how there are interesting connections with modern mathematics, for example random walks on groups, the theory of Frames and Fourier transforms. |