Tensorama

In our graduate careers, we encounter tensors in at least four guises:

(1) as presented in abstract-algebra texts;

(2) as multilinear functions (e.g. in differential geometry);

(3) as multidimensional arrays;

(4) as objects which transform in a certain way on change of coordinates
(physicists' favorite definition).

A bewildered first-year graduate student might well inquire: "Are these four
completely different things, all masquerading under the same name?"
Fortunately, that bewildered student has survived, more or less intact, into
his final year and is able to confidently report that they are in fact ALL THE
SAME THING. Wednesday at noon we'll see why, learn how to think about freedom
(freeness), and enjoy a bagel or two.

John Kerl
Graduate Student Colloquium
February 10, 2010