In the 1884 classic, "Flatland: A Romance of Many Dimensions," Edwin A. Abbott described a world where the inhabitants living in two dimensions are visited every millennium by an alien-like visitor from the world of three dimensions.  Although the book was written as a social satire, it does raise the interesting question whether there are extra dimensions that we are not currently aware of?  We shall analyse this question mathematically and see how the number and type of dimensions can have a big effect for statements in geometry.  We will also describe a new emerging understanding of the concept of dimension and explain why there might not be a simple answer to the question, how many dimensions do we live in?
The talk is accessible to all students. Pizza will be served.