# Malthe Sporring

I am a PhD student of Clark Barwick at the University of Edinburgh. I am interested in homotopy theory, in particular homotopy groups of spheres, chromatic homotopy theory, and (higher) category theory. I am also an experienced user of the online assessment system STACK. When I’m not thinking about mathematics I may be swing dancing, playing chess or photographing birds.

# Notes

Informal notes on various topics. Comments and corrections are welcomed. ### Chromatic homotopy theory

(January 2023) Notes for a seminar series on chromatic homotopy theory at the University of Edinburgh. Joint with Willow Bevington.

### Topological K-theory

(January 2023) Notes from a Winter 2023 eCHT graduate course on K-Theory. Joint with Adrián Doña Mateo and Willow Bevington.

### Persistent homology

(December 2022) Notes on persistent homology, as part of a GlaMS (Glasgow-Maxwell school) group project. Joint with Yan Yau Cheng and Adrián Doña Mateo.

### Axiomatic homology theory

(September 2021) Undergraduate notes on axiomatic homology theory. Homology is typically introduced as singular homology, with theorems proven explicitly using chain calculations. We take a different approach, defining a homology theory axiomatically as by Eilenberg and Steenrod, and then proving classical theorems directly from the axioms. This project was supervised by Prof. Clark Barwick and funded by the University of Edinburgh School of Mathematics Vacation Scholarship and College Vacation Scholarship funds.

# Talks

**Topological K-Theory**. Hodge Club (February 2023).**The ultrafilter monad**. GLaMS Example showcase (November 2022).

# Teaching

### Tutoring - Edinburgh

- (Spring 2023) Algebraic Topology
- (Spring 2023) Fundamentals of Pure Mathematics

# Reading groups and seminar series

- (2023)
**Eisenboaties.**A reading group on "The Rising Sea" by Ravi Vakil. Organised with Willow Bevington. - (2023)
**∞-categories.**A reading group on ∞-categories, following the book by Land. Organised with Willow Bevington and Adrián Doña Mateo. - (2023)
**Chromatic homotopy theory.**A seminar series at the University of Edinburgh, organised with Clark Barwick and Willow Bevington. - (2022-23)
**Eisenbuddies**. A reading group on commutative algebra, following the book by David Eisenbud. Organised with Willow Bevington.

# STACK

STACK is an open source online assessment system for STEM subjects. I have been involved in STACK since 2019 - here are some of my contributions:- Designing the STACK website stack-assessment.org.
- Editing a collection of case studies.
- Developing a video tutorial series.
- Designing STACK quizzes for The University of Edinburgh, Heriot-Watt University and The University of Glasgow.