Talks and Lectures
Find here the lecture notes and introductory lectures for my modules:
This course is about the linear theory of symmetries---ways that a group can act on a vector space by matrices. This is a surprisingly deep and ubiquitous theory, appearing throughout mathematics (algebra, geometry, number theory, analysis, ...) as well as physics. For a simple example, if you take a finite cyclic group, you discover that every way of acting by complex matrices can be put into diagonal form up to appropriate change of basis (really a statement about the Jordan Normal Form being diagonal if a matrix has some power equal to the identity).
This course is about the beautiful interplay---even dictionary---between algebra and geometry that you obtain by considering, as geometric objects, the zero loci of polynomial equations (in any number of variables). You will learn powerful tools to understand how they decompose into "irreducible" pieces of certain dimensions---curves in dimension one, surfaces in dimension two, etc. For a simple example, the "hyperbola" xy=1 can be put in bijection with the ground field take away zero: the value of x can be any nonzero number, and y is its inverse.
In Spring 2019 I taught a TCC course "Symplectic resolutions and singularities", meeting Thursdays 2-4 PM for eight weekly meetings commencing 17 Jan 2019.
Click here to access the Slack discussion forum for this course.