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February 23, 2018

Higher Algebra and Mathematical Physics

Posted by John Baez

You all know about Homotopy Type Theory Electronic Seminar Talks. Here’s another way to cut carbon emissions: a double conference. The idea here is to have a conference in two faraway locations connected by live video stream, to reduce the amount of long-distance travel!

Even better, it’s about a great subject:

  • Higher algebra and mathematical physics, August 13–17, 2018, Perimeter Institute, Waterloo, Canada, and Max Planck Institute for Mathematics, Bonn, Germany. Organized by David Ayala, Lukas Brantner, Kevin Costello, Owen Gwilliam, Andre Henriques, Theo Johnson-Freyd, Aaron Mazel-Gee, and Peter Teichner.

Higher algebra, lower carbon emissions… what more could you want?

Here’s the idea:

“Higher algebra” has become important throughout mathematics, physics, and mathematical physics, and this conference will bring together leading experts in higher algebra and its mathematical physics applications. In physics, the term “algebra” is used quite broadly: any time you can take two operators or fields, multiply them, and write the answer in some standard form, a physicist will be happy to call this an “algebra”. “Higher algebra” is characterized by the appearance of a hierarchy of multilinear operations (e.g. A-infinity and L-infinity algebras). These structures can be higher categorical in nature (e.g. derived categories, cohomology theories), and can involve mixtures of operations and co-operations (Hopf algebras, Frobenius algebras, etc.). Some of these notions are purely algebraic (e.g. algebra objects in a category), while others are quite geometric (e.g. shifted symplectic structures).

An early manifestation of higher algebra in high-energy physics was supersymmetry. Supersymmetry makes quantum field theory richer and thus more complicated, but at the same time many aspects become more tractable and many problems become exactly solvable. Since then, higher algebra has made numerous appearances in mathematical physics, both high- and low-energy.

Here are the speakers: Mina Aganagic *{}^\ast, Damien Calaque, Tobias Dyckerhoff, Davide Gaiotto, Dennis Gaitsgory, Lotte Hollands, Lisa Jeffrey, Mathilde Marcolli *{}^\ast, Greg Moore *{}^\ast, David Nadler, Adny Neitzke, Sylvie Paycha, Joerg Teschner, Bertrand Toen and Katrin Wendland. ( *{}^\ast means “to be confirmed”.)

Participation is limited. Some financial support is available for early-career mathematicians. For more information and to apply, please visit the conference website of the institute closer to you:

If you have any questions, please write to

Aaron Mazel-Gee told me:

We are also interested in spreading the idea of double conferences more generally: we’re hoping that our own event’s success inspires other academic communities to organize their own double conferences. We’re hoping to eventually compile a sort of handbook to streamline the process for others, so that they can learn from our own experiences regarding the various unique challenges that organizing such an event poses. Anyways, all of this is just to say that I would be happy for you to publicize this event anywhere that it might reach these broader audiences.

So, if you’re interested in having a double conference, please contact the organizers of this one for tips on how to do it! I’m sure they’ll have better advice after they’ve actually done it. I’ve found that the technical details really matter for these things: it can be very frustrating when they don’t work correctly. Avoiding such problems requires testing everything ahead of time — under conditions that exactly match what you’re planning to do!

Posted at February 23, 2018 6:43 AM UTC

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Re: Higher Algebra and Mathematical Physics

That seems to be the week for higher categories and physics. There’s a symposium (#109 here) – Higher Structures in M-Theory – organised by B. Jurčo, C. Saemann, U. Schreiber, and M. Wolf, taking place from August 12 - 18, 2018.

Posted by: David Corfield on February 23, 2018 7:46 AM | Permalink | Reply to this

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