This is the personal homepage of Kaveh Mousavand

In representation theory of algebras, my main focus of research, roughly speaking one understands the nature of an algebra via its action on some other algebraic structures, known as modules. An analogy I have made and often employ to explain this concept to non-mathematicians is the following. Experts may disagree with this analogy, but this is not for them anyway! 

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''Suppose you are given a stick A (which we may want to call an algebra) and this stick A is unfamiliar to you. Then, how would you develop some knowledge about it and how can you possibly determine whether the stick A is sturdy? 

You probably start by looking at its size, shape and some other physical properties. But, a lot of features of an object become clear only when we analyze its interactions with the other objects. In this case for instance, you may get to know about the unfamiliar stick A if you start hitting it against different objects that you already know and observe its influence on them. Obviously, your stick A cannot act on every arbitrary choice of object that may come to your mind. For example, you cannot hit a dream with it (at least as long as the stick itself is not a dream or part of it)! 
So, A can only act on certain objects whose nature is somehow compatible with that of your stick A.  From the action of A on each of these objects (which one can call an A-module) you get a better understanding of the strength of the stick A. 
To obtain a good knowledge of the sturdiness of A, sometimes one needs to examine A with respect to only finitely many other objects (A-modules) and sometimes one needs to hit infinitely many objects to get to know A more and more! Hence, one cay say some algebras (sticks) are easier to understand, where the complexity could be considered as the number of modules (objects) you need to hit to fully determine the strength of the stick!''