Introduction to algebraic topology with focus on the fundamental group and homology.
We consider ways of understanding aspects of Seiberg-Witten theory using a stable homotopy theory approach.We associate to the gauge theoretic situation a stable homotopy type. From this, we proceed by extracting information with the plethora of invariants coming from algebraic topology. This new way of looking at Seiberg-Witten has been used to reprove gauge theoretic results like Donaldson’s diagonalisation, the 11/8 theorem and the triangulation conjecture.
Introduction to linear algebra with applications from probability theory and optimisation.
Exercises on Webworks
Complex calculus focusing on methods for evaluating integrals over domains in the complex plane and the computation of various transforms and their application in engineering.
Homework1 Homework2 Homework3 Homework4 Homework5