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July 16, 2022

Conversations on Mathematics

Posted by John Baez

Now that I’ve retired, I have more time for pure math. So after a roughly decade-long break, James Dolan and I are talking about math again. Here are our conversations. Some are in email, but mainly these are our weekly 2-hour-long Zoom sessions, which I’ve put on YouTube. They focus on algebraic geometry — especially abelian varieties and motives — but also ‘doctrines’ and their applications to algebraic geometry, group representation theory, combinatorics and other subjects.

They may not be easy to follow, but maybe a few people will get something out of them. I have not corrected all the mistakes, some of which we eventually catch. I’ve added lots of links to papers and Wikipedia articles.

These conversations are continuing, but I won’t keep putting links to them here on nn-Category Café, so if you want more of them you can either check out my webpage at your leisure, or subscribe to my YouTube channel. I’ll probably fall behind in putting up videos, and then catch up, and then fall behind, etc. — so please don’t expect one to show up each week.

The conversations on YouTube are labelled ‘conversation’.

Posted at July 16, 2022 10:06 PM UTC

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Re: Conversations on Mathematics

Well, I said I wouldn’t update these, but I couldn’t resist it this time, because we just figured out something that we’d been leading up to in many conversations. James was puzzled by how the map sending smooth complex line bundles on a complex variety XX to elements of the vector space H 2(X,𝒪)H^2(X,\mathcal{O}) could have an image that’s “dust-like” — dense, but not the whole space. I finally did the calculation and showed that this really happens in an example! We still need to think about the consequences.

Posted by: John Baez on July 19, 2022 10:17 PM | Permalink | Reply to this

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