Deformation theory is not scary!

Deformation theory is one of the major successes of Grothendieck’s perspective on modern algebraic geometry, and is at the heart of cutting edge work in derived algebraic geometry. Despite being a subject that strikes fear into the heart of many a mathematician, the underlying concepts of deformation theory are unbearably simple. Indeed, it might be seen as an enormous generalization of the problem of understanding tangent spaces. Surprisingly, the deformation theory of an elementary object – an associative algebra over a field — is completely explicit and computable, and yet, illustrates many subtle aspects of the theory. In this talk, we will explore these ideas, and hopefully start to see what all the fuss is about.