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David Roberts
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### David Roberts

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http://arxiv.org/abs/1510.02402

Title: A user's guide to co/cartesian fibrations
Author: Aaron Mazel-Gee

Abstract:  We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely within the $\infty$-category of $\infty$-categories. We prove this is suitably compatible with the corresponding quasicategorical (and in particular, model-dependent) notions studied by Joyal and Lurie.

#arXiv   arXiv:1510.02402 ﻿
Abstract: We formulate a model-independent theory of co/cartesian morphisms and co/cartesian fibrations: that is, one which resides entirely *within the $\infty$-category of $\infty$-categories*. We prove this is suitably compatible with the corresponding quasicategorical (and in particular, ...
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The comparison to Grothendieck is not hyperbole if one views it as talking about relocating familiar objects into more general categories. For Grothendieck, it was generalising varieties to schemes in algebraic geometry. For Mochizuki it's generalising arithmetic objects to less familiar settings such as Frobenioids (cf the characterisation of anabelian schemes by their profinite fundamental groups).

Three years later, still not widely understood nor accepted. "The trouble that he faces in communicating his abstract work to his own discipline mirrors the challenge that mathematicians as a whole often face in communicating their craft to the wider world."

Via  at http://www.math.columbia.edu/~woit/wordpress/?p=8032﻿
A Japanese mathematician claims to have solved one of the most important problems in his field.
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Contrast with Tao's proof of the Erdös discrepancy problem, and even including the averaged Elliot conjecture that it relies on.﻿

### David Roberts

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Methinks some of the activities shown in this trailer, done in the pursuit of women's voting rights, would be these days labelled as terrorism.

The brief glimpse of the racehorse scene makes me wonder if the Emily Davison episode will be included: https://en.wikipedia.org/wiki/Emily_Davison

#foodforthought  ﻿
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Here is a (still rough) translation of the first half of the lecture, the Russian original is available from В. А. Рохлин Преподавание математики нематематикам I will hopefully finish the second ha...
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Wow. This is great. To think this talk was 30 years ago and we're still teaching economists limits before derivatives as if it helps. sigh﻿

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Thurston is one of the few mathematicians I know who never (as far as I can tell) wrote any incorrect statement, or made a conjecture that turned out to be wrong.

On being Thurstonized by Benson Farb

Being a Thurston student was inspiring and frustrating – often both at once. At our second meeting I told Bill that I had decided to work on understanding fundamental groups of negatively curved manifolds with cusps. In response I was introduced to the famous “Thurston squint”, whereby he looked at you, squint his eyes, give you a puzzled look, then gaze into the distance (still with the squint). After two minutes of this he turned to me and said: “Oh, I see, it’s like a froth of bubbles, and the bubbles have a bounded amount of interaction.” Being a diligent graduate student, I dutifully wrote down in my notes: “Froth of bubbles. Bounded interaction.” After our meeting I ran to the library to begin work on the problem. I looked at the notes. Froth? Bubbles? Is that what he said? What does that mean? I was stuck.

Three agonizing years of work later I solved the problem. It’s a lot to explain in detail, but if I were forced to summarize my thesis in five words or less, I’d go with: “Froth of bubbles. Bounded interaction.”﻿
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It is truly sad that Thurston was gone; he clearly had a serious broadband connection to the "truth"....﻿

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Being underrepresented in science, technology, engineering and math means women can be made to feel they don't belong, with long-term mental health consequences.
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More on The Erdős discrepancy problem

In my last post I wrote about the recent proof of this 80 year old conjecture by ​ . This new article explains the history behind the conjecture and gives a simple visualization of the problem with snakes and a precipice.

I can also recommend the video by ​

And most important on all - I now have a new math puzzle in my arsenal  - namely the 11 step version from the video. This 11 step possible very easy to explain to a ten+ year old and  can be solved with a little skill and some patience.﻿
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Have him in circles
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### David Roberts

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Sweet!

Via +Takayuki Kawamoto

Matriarch is a high-level language of materials architecture, implemented in an open-source Python library. Matriarch creates material architectures for protein structures and can output them as atomic configurations, in the form of PDB (protein data bank) files. Using Matriarch, an engineer can substitute building blocks and vary building instructions to create and study new materials.

The Matriarch language is based on the mathematical field of category theory, as discussed in the journal article, "A python library for materials architecture"; however, no knowledge of category theory is necessary to operate the program.﻿
| Home | About | Downloads | Gallery |. Matriarch. Authors: Ravi Jagadeesan, David Spivak, Tristan Giesa, and Markus Buehler. Matriarch is a high-level language of materials architecture, implemented in an open-source Python library. Matriarch creates material architectures for protein ...
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whoah...yeah!﻿

### David Roberts

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Some less-than-inventive spam accounts following me recently...﻿
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I've only ignored; haven't thought about actively reporting or blocking. However, it occurs to me that if we report, then it saves the rest of us having to check.

Oh, I see there's a mathematical optimisation problem here. Anyone care to have a go at finding the method that results in the best time savings, assuming 50 of us receive 3–5 fake follows per week, and it takes G+ 3 days to block an account? ;o)﻿

### David Roberts

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Fun stuff!

If you happen to be preparing a paper for the SODA proceedings (due a week from today), you might have noticed that the formatting macros have not changed in the past 19 years, despite their obvious formatting problems (so much for the added value of having a professional publisher). Fortunately, this means that the formatting macros I wrote some 15 years ago to fix some of these problems still work. I made some small changes this year to fix one more problem; here is the updated version.

To use this, add this file to your paper's folder and include the line \usepackage{sodafixes} in your LaTeX source. What it does:

- You no longer need to add explicit \Large formatting commands to your paper's title: it is formatted correctly automatically.

- The horizontal line at the top of the footnote listing your author acknowledgements no longer runs across the text of the footnote.

- Subsection headings now work, without having the subsection title run into the text of the following paragraph.

- Proofs now end with a Halmos box.

- There is no longer too much whitespace after the References section heading.

- (The new part that I just added:) the hyperref package's \autoref command now works for the theorem environment built into the SODA format. I only included this for theorems because for the others you can use \newcommand{\lemmaautorefname}{Lemma} as usual, but for some reason SODA defines theorems in a way that makes this harder to do.﻿
Some improvements to SODA proceedings format (ltexpprt.sty) %% David Eppstein, UC Irvine, 13 Oct 2000 %% Update 2015-10-07: make hyperref autoref work with theorem \makeatletter % Fix page offsets % \voffset-.75in \setlength{\oddsidemargin}{-1pc} \setlength{\evensidemargin}{-1pc} % Avoid having ...
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The Standard Model still holds up!

No deviations from the SM found.﻿
Abstract: The CMS and ATLAS collaborations searched for Dark Matter (DM) particles directly produced in pair. The searches are performed using the full LHC Run-I dataset recorded with the CMS and ATLAS detectors in proton-proton collisions at a center-of-mass energy of 8 TeV.
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### David Roberts

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After my talk in Paris [1] Patrick Iglesias-Zemmour kindly pointed me to Souriau 74 [2] for a flow chart highlighting the pre-quantization step in a similar manner to what I gave in [3]. I hadn't been aware of that particular article for some reason.

[1] http://ercpqg-espace.sciencesconf.org/?lang=en
[2] http://www.numdam.org/item?id=AIHPA_1974__20_4_315_0
[3] https://www.physicsforums.com/insights/higher-prequantum-geometry-need-prequantum-geometry/﻿
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:) or maybe is sad, Souriau invented geometric quantization, a long time ago.﻿
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