Hi, I am Felix Cherubini and this is my research website which was mostly written when I was working as a postdoc at Carnegie Mellon University (CMU) in Pittsburgh. After the postdoc, I took a full-time job in industry, which I reduced to 80% after the first month to have some time to enjoy pure mathematics. Currently, I am employed at the University of Augsburg. In October, I will start to work at the University of Gothenburg.

I am interested in application of Homotopy Type Theory (HoTT) to Differential and Algebraic Geometry and, more generally, I want to know how well HoTT can help to make current research in pure mathematics more understandable. The approach I am using is based on Urs Schreiber's differential cohesion.

In early 2018, I wrote an essay describing my thesis for the German competition "Klartext!". It didn't win and it is in German, you can view it here.

You can also go to the nLab.

More recently, my approach to the story includes the possibility to make calculations, which is possible in the Kock-Lawvere like axioms of synthetic algebraic geometry. I use some axioms which I know about from Ingo Blechschmidt's thesis and David Jaz Myers. You can watch the latest code here.

I organized a workshop called Geometry in Modal Homotopy Type Theory which took place March 11-15 2019 at CMU.

I gave a lecture on HoTT at the University of Augsburg in the summer 2021. There is a german script.

Modal Descent with Egbert Rijke, accepted 2020 for publication in MSCS, arxiv, (doi: 10.1017/S0960129520000201)

Cartan Geometry in Modal Homotopy Type Theory, preprint, 2018, arxiv, git

Cohesive Covering Theory extended abstracts for the Workshop "Homotopy Type Theory and Univalent Foundations" in Oxford 2018

Formalizing Cartan Geometry in Modal Homotopy Type Theory, PhD-thesis, 2017, KIT library, git

Differential Cohesive Type Theory with Jacob A. Gross, Daniel R. Licata, Max S. New, Jennifer Paykin, Mitchell Riley, Michael Shulman. extended abstracts for the Workshop "Homotopy Type Theory and Univalent Foundations" in Oxford 2017

Here is an overview of video recordings of talks about my topics:

In March 2018 I gave an overview talk during the MURI-meeting (part 1 part 2).

Together with Dan Licata, I gave a tutorial at the workshop on Homotopy Type Theory during the Hausdorff Trimester on Types, Sets and Constructions. It was about Modal Homotopy Type Theory and there are recordings on Youtube listed below. What I write on the blackboard is even less readable than usual though.

This one might be the best place to start, if you want to understand the general direction of what I am interested in.

This one focuses on the cartan geometry from my thesis.

Those were tutorials 2 and 6, here is the complete list:

Tutorial 1 Dan Licata: A Fibrational Framework for Modal Simple Type Theories

Tutorial 2 Felix Wellen: The Shape Modality in Real cohesive HoTT and Covering Spaces

Tutorial 3 Dan Licata: Discrete and Codiscrete Modalities in Cohesive HoTT

Tutorial 4 Felix Wellen: Discrete and Codiscrete Modalities in Cohesive HoTT, II

Tutorial 5 Dan Licata: A Fibrational Framework for Modal Dependent Type Theories

Tutorial 6 Felix Wellen: Differential Cohesive HoTT

- I also gave a talk (on workshop website) at the workshop linked above.

You can use the address felix.cherubini[at]posteo.de to contact me. There is also a pgp-key for this address with fingerprint 63E6 E9E2 D88A 267B 7A44 5A34 62D3 070A CDC1 004E

Ressources and notes that are probably only of use to myself.