Martin Speirs

Postdoc at UC Berkeley Maths department. Funded by the Independent Research Fund Denmark.

I completed my PhD at the University of Copenhagen in November 2018. My advisor was Lars Hesselholt. My research is in Algebraic Topology and Arithmetic Geometry. More specifically I am interested in: Topological Hochschild homology (and all of its many related theories), equivariant stable homotopy theory, p-adic cohomology theories, p-adic Hodge theory, algebraic K-theory, Witt vectors and de Rham-Witt complexes.

In my PhD thesis I use the methods developed by Nikolaus and Scholze to make computations of algebraic K-theory using topological cyclic homology. The new framework greatly simplifies previous calculations and allows new ones as well.

For more information please see my: CV

Geography

Starting in the 2019 fall semester I will be a postdoc at UC Berkeley. 

During the 2019 spring semester I was at MSRI in Berkeley as a postdoc in the derived algebraic geometry semester.

Research papers

1.  On the  K-theory of coordinate axes in affine space. Submitted. Available here: https://arxiv.org/abs/1901.08550

2. On the  K-theory of truncated polynomial algebras, revisited. Submitted. Available here: https://arxiv.org/abs/1901.10602

Conferences and organizing

March 1-6 2019 I was at the Arizona Winter School (AWS) in Tucson as study group assistant for Matthew Morrow’s lectures on THH and arithmetic geometry. The notes and videos of his talks are on the website. I made a few “reading projects” to guide students through the material, they are available here

I helped compile the report for the Oberwolfach Arbeitsgemeinschaft on Topological Cyclic Homology, April 2018. It is available here.

June 2017 I co-organized a masterclass in Copenhagen on stable homotopy theory and p-adic Hodge theory. Check out the notes from the two great lecture series.

July 2016 I co-organized the Young Topologists Meeting in Copenhagen.

Previous work

My master’s thesis Model Categories; With A View Towards Rational Homotopy Theory dealt with Quillen’s theory of model categories as it is exemplified in his work on algebraic models of rational homotopy theory. The thesis was supervised by Kristian Moi.

In 2013 I wrote some notes on model theory (in the sense of logic) that I prepared for a course given by Thomas Scanlon at Berkeley.

Contact

mps (at) berkeley.edu       or       speirs (at) math.ku.dk   

UC Berkeley maths dept., Evans Hall, Room 987

Mathematical Sciences Research Institute, Room 202

Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark,

Building 4, Room 4.03.