The purpose of these notes, as suggested by the title, is not to provide any sort of comprehensive introduction to deformation theory. Rather, we attempt to convey the main ideas of the theory, with a survey of some applications. We do not explore an exhaustive list of possible topics, nor do we go into details in many proofs. However, in the case of deformations of smooth varieties we do attem...

Recently, the invertibility of linear combinations of two idempotents has been studied by several authors. Let P and Q be idempotents in a Banach algebra. It was shown that the invertibility of P + Q is equivalent to that of aP + bQ for nonzero a, b with a + b 6= 0. In this note, we obtain a similar result for square zero operators and those operators satisfying x = dx for some scalar d. More g...

An order is a commutative ring of which the additive group is a finitely generated free abelian group, and a graded order is an order that is provided with a grading by some abelian group. Examples are provided by group rings of finite abelian groups over rings of integers in number fields. We generalize known properties of nilpotents, idempotents, and roots of unity in such group rings to the ...

We compute the Kauffman skein module of the complement of torus knots in S3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2, C)-characters tensored with the ring of Laurent polynomials. Skein modules were introduced indenpendantly by V. Turaev in 1988 and J. Przytycki in 1991 (see [TU88, HP92]) as a C[A±1]-module associated to a 3-manifold M generated by banded link...