[Alta-Logic] Peripatetic Seminar for 07 March 2025

[Geoff Vooys]

Hi Everybody,

Today in the Peripatetic Seminar one of two things will happen: first, either I will give a talk on tangent categories and ways to categorically capture what makes morphisms immersions, submersions, local diffeomorphisms, and other such things (depending on time and with the caveat that I want things to be understandable, so the pace will be gentle and with running examples). Second, Robin may give a talk on something of his choosing should he feel the desire. In either case, I'm looking forward to seeing you all at 14:00 in ICT 616.

Cheers,
Geoff

Title: Immersions, Submersions, and Local Diffeomorphisms Categorically, Oh My!

Location: ICT 616

Time: 14:00 Mountain Standard Time 

Abstract: Tangent categories are a categorical abstraction of the structural properties of differential geometry as incarnated by the tangent bundle first discovered by Rosicky in 1984 and then later rediscovered and extended by Cockett and Cruttwell in 2014. In the last decade, research in tangent categories has proceeded rapidly and shown to have myriad and insightful interactions with many areas of mathematics, computer science, logic, physics, and more. Of particular interest to me is the fact that tangent categories provide a bridge through which the categorically-minded may understand both algebraic geometry and differential geometry (and in ways that are categorically sound, i.e., developed without pretending schemes are manifolds or that manifolds are schemes).

In this talk I will introduce many of the ideas involved in tangent categories as well as how to incarnate the notions of immersions, submersions, and local diffeomorphisms from the categorical framework. Some of this talk (effectively anything I present which is yet-to-be-published) is based on joint work with JS Lemay.
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