Teaching

Current Teaching

This term I am teaching:
MAU34106 - Galois Theory

MAU22E02 - Engineering Mathematics IV

More information about these courses can be found on their respective pages, which will be updated regularly throughout the term. For MAU22E02, students should refer to the module page on Blackboard

Recent Teaching

Last term I taught:
MAU22103/MAU33101 - Introduction to Number Theory

MAU22203/MAU33203 - Analysis in Several Real Variables

More information about these courses can be found on their respective pages.

Past Teaching

MMG710 Fourier Analysis - Gothenburg University LP1 2023
A complete set of notes can be found here, and a complete set of exercises can be found here.

Multiple zeta values and motivic periods - University of Bonn WS21/22
Partial notes from this course can be found here.

Multiple zeta values are natural generalizations of values of the Riemann zeta function at integer argument to multiple variables. They have been studied at least since Euler, and, unlike single zeta values, are known to satisfy many algebraic relations. Furthermore, they arise naturally in many different contexts (mixed Tate motives, quantum groups, moduli spaces of vector bundles, knot theory, associators, etc.) An important open problem is to determine the dimensions of the space of multiple zeta values of a given weight and depth. This is a challenging problem in transcendence theory, but can be essentially solved motivically.

We can write MZVs as iterated integrals on the projective line minus three points and can thus lift them to motivic periods. These motivic analogues form a graded Q-algebra which maps surjectively onto the Q-algebra of multiple zeta values, This motivic algebra comes with additional algebraic structures which can be used to define a motivic basis (Brown), providing a partial answer to the above problem.

The goal of this course is to give an introduction to (motivic) multiple zeta values and motivic periods, alongside the machinery necessary to proof Brown's result giving a basis for motivic MZVs. As this can be quite technical, some aspects of the theory will only be presented in their simplest forms. Lecture notes will be made available shortly after each lecture.

There are no prerequisites, but some familiarity with schemes, basic category theory, and cohomology would be beneficial