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The mathematics of the 21st century

John BaezJohn Baez
edited February 7 in Applied Category Theory Seminar

The first talk of our seminar is now available to watch and discuss!

January 8, 2019: John Baez - The Mathematics of the 21st century

Abstract. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics - and be affected by it - just as dramatically as the agricultural revolution or industrial revolution. We should get ready!

Watch the video while also looking at the talk slides. For more information click on the links in green. Ask me questions either here or on the Azimuth Blog, where we already have a discussion starting!

Also try these slides and videos from related talks:

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    1.
    Pierre Prado

    Hi John, on your slides you cited "To understand ecosystems, ultimately will be to understand networks. — B. C. Patten and M. Witkamp"

    Could you please share your thoughts, and references perhaps, about if/how this central role of networks resonates with Topology ? Is it an ultimate framework layer to you? And how important/useful could it be regarding studying Earth system ?

    Thanks in advance, best

    Comment Source:Hi John, on your slides you cited "To understand ecosystems, ultimately will be to understand networks. — B. C. Patten and M. Witkamp" Could you please share your thoughts, and references perhaps, about if/how this central role of networks resonates with Topology ? Is it an ultimate framework layer to you? And how important/useful could it be regarding studying Earth system ? Thanks in advance, best
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    2.
    WebHubTelWebHubTel

    re "... Topology ? Is it an ultimate framework layer to you? And how important/useful could it be regarding studying Earth system ?"

    Condensed matter physicists are making great progress in climate science via topological modeling:

    Delplace, Marston, Venaille: Topological Origin of Equatorial Waves

    "Topological effects that arise from material boundaries are well known in solid-state physics and form the basis for topological insulators. Delplace et al. describe atmospheric and ocean waves that appear to have a similar topological origin. The waves exist because of the symmetry-breaking nature of Earth's rotation, which allows certain fixed topological constraints on the system. These findings may be useful for understanding a wide variety of geophysical and astrophysical flows."

    Quanta Magazine: Mathematicians Tame Turbulence in Flattened Fluids

    "By squeezing fluids into flat sheets, researchers can get a handle on the strange ways that turbulence feeds energy into a system instead of eating it away."

    To understand the role of condensed-matter physics in applied physics, this is an interesting read from last week's Physics Today: When condensed-matter physics became king

    "The story of how solid-state physics emerged in the postwar period and was eventually rebranded as condensed-matter physics illuminates some major shifts in the late-20th-century physics community."

    Comment Source:> re *"... Topology ? Is it an ultimate framework layer to you? And how important/useful could it be regarding studying Earth system ?"* Condensed matter physicists are making great progress in climate science via topological modeling: Delplace, Marston, Venaille: [Topological Origin of Equatorial Waves](http://science.sciencemag.org/content/358/6366/1075) > "Topological effects that arise from material boundaries are well known in solid-state physics and form the basis for topological insulators. Delplace et al. describe atmospheric and ocean waves that appear to have a similar topological origin. The waves exist because of the symmetry-breaking nature of Earth's rotation, which allows certain fixed topological constraints on the system. These findings may be useful for understanding a wide variety of geophysical and astrophysical flows." Quanta Magazine: [Mathematicians Tame Turbulence in Flattened Fluids](https://www.quantamagazine.org/mathematicians-tame-turbulence-in-flattened-fluids-20180627/) > "By squeezing fluids into flat sheets, researchers can get a handle on the strange ways that turbulence feeds energy into a system instead of eating it away." To understand the role of condensed-matter physics in applied physics, this is an interesting read from last week's Physics Today: [When condensed-matter physics became king](https://physicstoday.scitation.org/doi/full/10.1063/PT.3.4110) > "The story of how solid-state physics emerged in the postwar period and was eventually rebranded as condensed-matter physics illuminates some major shifts in the late-20th-century physics community."
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    3.
    Pierre Prado

    Thanks Paul Pukite..very interesting refs..

    Comment Source:Thanks Paul Pukite..very interesting refs..
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    4.
    Pierre Prado
    edited January 15

    https://ncatlab.org/nlab/show/Top and https://ncatlab.org/nlab/show/nice+category+of+spaces cool..

    Comment Source:https://ncatlab.org/nlab/show/Top and https://ncatlab.org/nlab/show/nice+category+of+spaces cool..
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    5.
    WebHubTelWebHubTel

    Here is one Azimuth thread that is currently discussing the climate behaviors that may have topological origins

    QBO and ENSO

    Comment Source:Here is one Azimuth thread that is currently discussing the climate behaviors that may have topological origins [QBO and ENSO](/discussion/1471/qbo-and-enso#latest)
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