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Hi, I am Felix Wellen and this is the research website 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.

What my research is about

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.

Events

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

Written work

  • Modal Descent with Egbert Rijke, article in peer review, 2019, no pdf for download yet.
  • Cartan Geometry in Modal Homotopy Type Theory, article in peer review, 2018, most recent, 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

Videos

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 genral 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

You can use the address felix.wellen[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

Date: 2018-11-13 Tue 00:00

Author: Felix Wellen

Created: 2019-06-23 Sun 13:02