The main goal of this seminar is to understand Urs Schreiber’s work Differential cohomology in a cohesive infinity-topos and other related material.
This seminar is inspired Exodromy. We aim for informal talks, and we can take as much time as we need. This group can last for an extended period so that we can have time to work on more content.
We run our group more asynchronous and flexible: the speakers can choose the lecture time as they want or record a video by themselves, and then we put the record online. Everyone who wants to participate can fill the form (or see below) and join our Discord. You can also contact me by by mail.
Because we can plan for this group to continue for some time, we can work and discuss some advanced and not so well-known prerequisites, like higher topos theory. My point is that we do not need to be experts for using them in [DCCIT]. Instead, we can first try to have rough pictures, know what they are, and keep some examples in mind. Then we can use them to read further texts, like here [DCCIT]; in that process, we can gradually realize the details we missed. That is also the goal of this seminar. We also list some helpful resources below for you.
Of course, there are some things that we assume to be known, like the basics of category theory, differential geometry and algebraic topology. But if you don't have confidence in those, don't worry, since it is often enough to just know the basic idea in many cases, and we will later give them new interpretations at a higher level as we progress. On the other hand, since these prerequisites are well-known and classical, there is a lot of material, and it is not too hard to brush up on the basics, so it should be possible to quickly catch up.
EPIT Spring School on Homotopy Type Theory, videos
Higher Algebra, Homotopy Theory Münster, videos
Topos à l'IHES, videos
especially, Urs SCHREIBER - Synthetic prequantum field theory in a cohesive homotopy topos, paper, video
Felix Wellen, The Shape Modality in Real cohesive HoTT and Covering Spaces, video
Felix Wellen, Discrete and Codiscrete Modalities in Cohesive HoTT, video
Felix Wellen, Differential Cohesive HoTT, video
Felix Wellen, Formalizing Cartan Geometry in Modal Homotopy Type Theory, thesis updated thesis
Michael Shulman, Homotopy type theory: the logic of space, paper
Michael Shulman, Brouwer's fixed-point theorem in real-cohesive homotopy type theory, paper
A Synthetic Approach to the Formal Theory of PDEs, paper, video
rough schedule, we are still planning...