Nicolaus Heuer

                 

This is my mathematical webpage. To see my professional website, please see my LinkedIn profile.

         

About myself

I am a mathematician who was working in geometric group theory. I previously obtained my PhD from Oxford and was a PostDoc in Cambridge. I am especially interested in constructing and computing invariants which detect coarse manifestations of non-positive curvature. Such invariants are stable commutator length, simplicial volume and bounded cohomology. Please see my (academic) CV (June 2020) for my academic biography. If you like to know what I did, please see my research statement (from February 2019). As to the question of why I did it, here is an introductory note about stable commutator length which was the focus of most of my research.

From February 1st 2021 on I will be enjoying early retirement from academia as I move to Finance/Data Science. I would like to take the chance to thank everyone I met and everyone who supported me in the last five years of academia - Thank you! I am keeping this site to keep my code, my papers and my contact details. Please drop me an email if you like to talk about stable commutator length and bounded cohomology - and even if you want to talk about something entirely different!

         

Publications & Preprints

All of my papers are available on my arXiv page.

Thesis

1. Constructions in Stable Commutator Length and Bounded Cohomology. PhD Thesis, Oxford (2019) under the supervision of Martin Bridson

Publications

1. Low-dimensional bounded cohomology and extensions of groups. Mathematica scandinavica 126.1 (2020): 5-31.
2. Cup Product in Bounded Cohomology of the Free Group. Ann. Scuola Norm. Sci. (To appear).
3. Spectral gaps in scl for amalamated free products and RAAGs. Geom. Funct. Anal. (2019) 29: 198.
4. The spectrum of simplicial volume. Joint with Clara Löh. Inventiones mathematicae (2020): 1-46.
5. Transcendental simplicial volumes. Joint with Clara Löh. Annales de l'institut Fourier (To appear)
6. The full spectrum of scl on recursively presented groups. Geometricae Dedicata (to appear)

Preprints

1. Spectral gap of scl in graphs of groups and 3-manifolds. Joint with Lvzhou Chen. Preprint Oct 2019.
2. Simplicial volume of one-relator groups and stable commutator length. Joint with Clara Löh. Preprint Nov 2019.
3. Computing commutator length his hard. Preprint Jan 2020.
4. The spectrum of simplicial volume of non-compact manifolds. Joint with Clara Löh. Preprint Nov 2020.
5. What is stable commutator length?. A note I wrote for the International What is..? Seminar on Simplicial Volume and Bounded Cohomology. Nov 2020.
6. Stable commutator length in right-angled Artin and Coxeter groups. Joint with Lvzhou Chen. Preprint Dec 2020.

         

Miscellaneous

1. Talks.
2. Teaching.
3. Posters and Presentations.
4. Code.
5. I am one of the organizers of the International Young What Is Seminar In Simplicial Volume and Bounded Cohomology.
6. Contact Details.

 

         

Latest Update: 09.12.20