Timeline for "Next steps" after TQFT?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 3, 2023 at 0:49 | comment | added | David White | @IanAgol when you say "Laurie" do you mean "Lurie"? Also, the Cobordism Hypothesis is due to Baez and Dolan, but Lurie sketched a proof of it. | |
| Jun 28, 2023 at 4:11 | history | edited | Nicholas James | CC BY-SA 4.0 |
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| Jun 26, 2023 at 20:08 | comment | added | Dmitri Pavlov | The question asks about “new genres to take a look at”, one example is nontopological functorial field theory, see people.mpim-bonn.mpg.de/teichner/Math/ewExternalFiles/…, and, more recently, arxiv.org/abs/2011.01208 and arxiv.org/abs/2111.01095. | |
| Jun 26, 2023 at 19:24 | history | edited | Nicholas James | CC BY-SA 4.0 |
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| Jun 26, 2023 at 15:29 | comment | added | Ian Agol | A big topic is a restricted notion of TQFT: and extended topological field theory. The main activity here is to try to give a complete proof of Laurie’s cobordism hypothesis. This is mostly under the auspice of homotopy theory and differential topology. en.m.wikipedia.org/wiki/Cobordism_hypothesis | |
| Jun 26, 2023 at 14:16 | history | edited | Nicholas James | CC BY-SA 4.0 |
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| Jun 26, 2023 at 9:59 | comment | added | Abdelmalek Abdesselam | I think a good resource to learn what is currently going on in the area of TQFT is scgcs.berkeley.edu and in particular the "events" tab. For example you can find a recent summer school listed there categorified.net/TQFT2023 with lecture notes etc. There are more events coming up, so you might want to ask the organisers if you could attend. | |
| Jun 26, 2023 at 8:29 | comment | added | JP McCarthy | Along similar lines to the above comment, find your favourite TQFT paper, type its title into Google Scholar, and look at "cited by". Repeat. | |
| Jun 26, 2023 at 7:57 | history | edited | YCor | CC BY-SA 4.0 |
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| Jun 26, 2023 at 4:09 | comment | added | Buzz | The holy grail of TQFT would be a prescription for the duality that interchanges the operator quantum numbers and topological quantum numbers of an arbitrary QFT. More prosaically, there is the sub-problem of finding dualities between classes of perturbative intractable QFTs and (inherently nonperturbative) TQFTs. | |
| Jun 26, 2023 at 4:01 | comment | added | Alec Rhea | Presumably you're familiar with the relationship between string theory and TQFT? | |
| Jun 26, 2023 at 3:24 | comment | added | Nicholas James | @RyanBudney: Thank you for the reply! What I meant by "comes after" was this: what has it been applied to in recent years (and are there resources to learn about these new applications?), is it actively researched today and if so in what areas, what new genres or topics have been built off of it in recent years (and are there any resources to learn about these new advances?), etc. Hopefully that clears things up, I hope my question is less ambiguous and easier to answer now. | |
| Jun 26, 2023 at 3:17 | comment | added | Ryan Budney | I'm not certain what you mean by "comes after". Are you referring to a specific person's temporal narrative? What generally comes "after" is whatever you take an interest in, i.e. the linear narrative should be your own. | |
| Jun 26, 2023 at 2:59 | history | asked | Nicholas James | CC BY-SA 4.0 |