Colloquium: Matrix permanents
by Dr Ian Wanless
Abstract: The permanent is a function on matrices, from the same family as the determinant. Since being introduced by Cauchy in 1812, it has found a wealth of applications in areas like probability, particle physics, algebra and combinatorics. For example, the permanent arises in many counting problems that involve permutations or matchings in bipartite graphs. Much of the 20th century study of permanents was driven by
van der Waerden's conjecture about which doubly stochastic matrix minimises the permanent. This "simple" conjecture took over 50 years to solve, and in the meantime spawned several related conjectures that remain open to this day. This colloquium will give a general overview of the study of permanents. It will survey some of the most important known results and interesting open problems. The survey will be broad rather than deep, and hence suitable for non-specialists.
For More Information: Contact Paul Pearce (P.Pearce@ms.unimelb.edu.au) or Paul Norbury (P.Norbury@ms.unimelb.edu.au)