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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2022

    I am taking the liberty of creating a category: reference-entry in order to have a way to hyperlink references to our new research center here in NYUAD, which is slowly but surely entering into tangible existence.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2022

    have now added speakers, titles and abstracts for our first little workshop (public on zoom) which might be of interest to some readers here:

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 21st 2022

    Wasn’t there a mission statement some place? Was it the article, Sati and Schreiber 2021: ’Topological and Quantum Systems’, mentioned at computational trilogy?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2022

    Besides whats in the nLab entry now, there is the following paragraph on the center landing page here (the domain nyuad.nyu.edu seems to have a hiccup right now, does it work for you?):

    The Center for Quantum and Topological Systems serves as a nucleation point for cross-disciplinary expertise in theory and application of Quantum Topological Systems in general, with an emphasis towards the unifying goal of robust Quantum Computation in particular — combining all questions from theoretical foundations (quantum error-correction) over hardware (topological quantum materials and novel quantum chips), architecture (parameterized quantum circuits) and software (quantum programming languages and hardware-aware software optimizations) to applications (quantum machine learning and quantum cryptography)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 26th 2022

    have added (here) the remaining title+abstract for the TDA workshop next week

    diff, v7, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 29th 2022

    added a section (here) for the Geometry, Topology and Physics-seminar, with a list of the past talks (most of them with links to zoom recordings)

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 9th 2022

    have added pointer to the upcoming external talk:

    \,

    Also, I am eager to add the list of names of our group of postdoc researchers who are arriving in the next weeks (or have already), but don’t want to say anything that may not be fully official yet. What I can safely say is that among them are are Adrian Clough, David Jaz Myers and Mitchell Riley.

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 9th 2022

    Great team! Let me know when you need a philosopher.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2022

    added the list of members (here)

    diff, v18, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 14th 2022

    have added pointer (here) to: Initial Researchers’ Meeting – Motivation, Strategy & Technology (pdf)

    diff, v20, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2022

    added pointer (here) to:

    diff, v21, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeSep 16th 2022

    added pointer (here) to:

    diff, v22, current

  1. Updated the details of Adrian Clough’s talk of 2022-10-05.

    Adrian Clough

    diff, v30, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeApr 20th 2023

    have now finished uploading the slides and video recordings of the “QFT and Cobordism”-meeting last month: here

    diff, v181, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeSep 8th 2023
    • (edited Sep 8th 2023)

    with the summer break over, we are resuming next week. In the GTP-seminar wel’ll have:

    As before, I’ll add (here) resources as they become available

    diff, v204, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2024

    schedule, titles and abstracts for “Running HoTT 2024” now listed here

    diff, v319, current

    • CommentRowNumber17.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 17th 2024
    • (edited Apr 17th 2024)

    Looks like a great conference.

    Your abstract had me remember those ideas on jet \infty-toposes approximating twisted cohomology:

    Higher-order approximations should involve a notion of higher-order forms of the tangent (∞,1)-topos, in parallel with the relationship between the jet bundles and tangent bundle of a manifold. It is clear that whatever we may say in detail about the kkth-jet (∞,1)-topos J kHJ^k\mathbf{H}, its intrinsic cohomology is a version of twisted cohomology which is in between nonabelian cohomology and stable i.e. generalized (Eilenberg-Steenrod) cohomology.

    It seems that a layered analysis of nonabelian cohomology this way in higher homotopy theory should eventually be rather important, even if it hasn’t received any attention at all yet. It seems plausible that a generalization of Chern-Weil theory which approximates classes of principal infinity-bundles not just by universal characteristic classes in ordinary cohomology and hence in stable cohomology, but that one wants to consider the whole Goodwillie Taylor tower of approximations to it.

    If the first approximation prompts extension of HoTT to linear HoTT, is there some ’twisted HoTT’ out there?

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2024

    The twisting of cohomology seen in an \infty-topos just corresponds to dependency of the types in the corresponding internal logic. In this sense plain (L)HoTT is already “twisted”.

    In the paragraph you quote it is not the twisting that makes the difference, but the “degree of linearity” of what is being twisted.

    • CommentRowNumber19.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 18th 2024

    Ah, OK. So what makes the first degree of linearity stand out as so central to quantum physics?

    What would, say, second degree linearity relate to?

    • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2024
    • (edited Apr 18th 2024)

    The degree kk in J kHJ^k \mathbf{H} refers to Goodwillie polynomials of degree kk.

    By all that is known, coherent quantum processes are linear maps, not more general polynomial maps or worse.

    (This reminds me of how Maxim Kontsevich trolled the 2015 Breakthrough Prize ceremony by declaring that the universe must be a simulation because it is “impossible” that quantum physics is really about linear spaces instead of curved manifolds like the rest of physics — around 19:30.)

    • CommentRowNumber21.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 18th 2024

    Funny. Fine to present it as a source of bafflement, but the step to simulation seems bizarre.

    • CommentRowNumber22.
    • CommentAuthorperezl.alonso
    • CommentTimeApr 18th 2024

    So what is the more precise statement about linearity here? Would it be “coherent quantum processes observable to an observer are linear maps”? This reminds me of the recent series of papers by Witten (e.g. this) where one describes an algebra of observables (hence linear) only in relation to an observer (there described by a timelike curve).

    • CommentRowNumber23.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2024

    Not sure what you are after here. Coherent quantum processes are unitary linear operators between Hilbert spaces. That’s essentially one of the axioms of QM.

    • CommentRowNumber24.
    • CommentAuthorperezl.alonso
    • CommentTimeApr 18th 2024

    Maybe I’m misunderstanding what you are referring to as quantum physics, since what I mentioned is supposed to be an observation of quantum gravity. I guess the question is, doesn’t quantum gravity (understood as a generalization of qft, not as a class of qft’s) take those higher degrees kk into account? In the sense you mention an axiom of QM is restricting to order k=1k=1, isn’t the point of QG that one of the to-be axioms is the incorporation of those higher degrees?

    • CommentRowNumber25.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2024

    No, quantum gravity is not meant to change the rules of quantum physics. Those C *C^\ast-algebras of quantum observables that you point to are still (embedded into) algebras of linear operators.

    • CommentRowNumber26.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2024
    • (edited Jul 10th 2024)

    video recordings of all talks at Running HoTT 2024 now available: find the link below the corresponding speaker/title in the list here

    diff, v350, current