Abstract: Suppose that you have n kids sitting around a round table, each with a bowl of cereal in front of him/her. As soon as the teacher turns away, each kid steals half of the cereal of his neighbor to the right and half of the cereal of his neighbor to the left, putting it in his own bowl, while the neighbors are doing the same thing to him. Is it true that if the teacher turns away sufficiently many times, we will get an even distribution, with each kid having about the same amount of cereal? And if so, how fast will the distribution be converging to the uniform one?
This problem can be solved by brute force, but the solution can be greatly simplified if we observe that the problem has a nice symmetry: it is unchanged if we rotate the table.
Of course, it is a toy problem. but the same idea of using symmetries can be applied in many other problems; the proper language for this is the language of groups and their representations. We will discuss the basics of this theory and explain how it can be applied to solving various problems, from kids eating cereal to the spectrum of the hydrogen atom in Bohr’s model.
The talk assumes that you have a good knowledge of linear algebra and are familiar with the definition of a group.
