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David Roberts
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David Roberts

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Sharing so that I can keep a tab on the discussion in the comments. It seems someone has already knocked 2000-ish symbols off the original Turing machine described by Aaronson and Yedidia, and bypassing Friedman's recent work on undecidable Pi-0-1 statements (which are equivalent to consistency of certain large cardinals, so complete overkill) in the process.
 
Take a Turing machine with n states, two symbols, and a blank tape. What's the longest it will take to halt, if it ever does? That's the nth busy beaver number, BB(n). This sequence grows really fast and is wildly uncomputable. Now Scott Aaronson and Adam Yedidia have a paper showing that BB(7918) is unknowable within ZFC set theory!
I've supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. Today, I'm proud to announce that Adam Yedidia, a PhD student at MIT (but an MEng student when he did most of this work), ...
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What's this result worth?

I ended up answering my own question on extension of smooth functions on manifolds here

http://mathoverflow.net/a/238067/4177

with an answer going far beyond what I imagined possible, but I have no feeling for how such a result would be viewed by people who are experts in the area: is this a trivial application of known results, such as might just be one part of the proof of the intended end result (this extension result is but one needed step of a longer proof), or something worth writing about for its own worth? If the latter, I can imagine also finding quantitative estimates etc, but that's going far beyond what I need. If such a thing interests you, however, let me know. The general stuff about maps between metric spaces that preserve interior corkscrew domains should be of general interest, I would hope.

Actually, I should say that I'm not really interested in showing

C^∞(M)→C^∞(K)

is a split surjection of Fréchet spaces, but the global result that C^∞(M,Y)→C^∞(K,Y) is a submersion of Fréchet manifolds. This is what I need for constructions of mapping stacks.
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+Alexander Schmeding that's the plan. I need to sit down and do the proof for the submersion, now that I have the local result :-)
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sigh... I once played a Pärt piece (the Ostinato from opus 2) with a small amount of impressive octave work, but never anything approaching this level of vigour.
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Another semester of graduate algebra is in the can.

This time I learned/taught about linear algebra and modules from the categorical point of view (and in the process converted myself to the categorical way of thinking).

Over the course of two semesters I produced 642 pages of hand-written lecture notes and 87 pages of typed homework/exam solutions, all of which can be found at these two webpages:

http://www.math.miami.edu/~armstrong/761fa15.html
http://www.math.miami.edu/~armstrong/762sp16.html

Why did I do this? I suppose in the hope that someone other than myself and the 12 students in the room might benefit from my struggles to understand this material.

Enjoy.
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Swansea mathematics is hiring. Anyone interested or know postdocs who might be interested? 
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...'we have money - > transforming them into computers - > then the right candidate transforms computers into (mathematical) glory - > then glory makes more money' ...it seems homological algebra is very useful in understanding how math looks from outside ... it was fun to read, thanks for sharing :-) .
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Just finished refereeing a paper that is essentially a sequence of nasty calculations in bicategories spread over a few dozen pages... Phew. Now to write the report and recommend more diagrams be used, instead of inline (or rather multiline) equations.
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Given that publishers don't really handle the review process directly, I'm guessing +Paul Bryan​ meant the editor.
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...he also cites Gauss, Kronecker and Poincare
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It's always been a bit of a mystery why the polynomial method, which has had many impressive successes in the incidence geometry of finite field vector spaces, has not been able to make progress on the capset problem (bounding the size of subsets of Z_3^n that are free of three-term arithmetic progressions). In this paper of Croot, Lev, and Pach, they manage to use the polynomial method to get a surprisingly strong bound for the analogous problem in Z_4^n (far surpassing the Fourier-analytic techniques which have long held the title to best bounds for these Roth theorem type results). Currently the method is restricted to the 4-torsion case, but it gives hope that some other deployment of the polynomial method could be effective for other groups, and particularly for the capset problem. #spnetwork arXiv:1605.01506
Selected Papers Network
Progression-free sets in Z_4^n are exponentially small. Ernie Croot, Vsevolod Lev, Peter Pach. We show that for integer $n>0$, any subset $A \subset Z_4^n$ free of three-term arithmetic progressions has size $|A|<2(\sqrt n+1) 4^{c n}$, with an absolute constant $c \approx 0.926$.
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The article does wait until half-way through to comment on Cheng's appearance, but that may be for the benefit of non-sighted people, since otherwise people can clearly see what she looks like from the photos -- including, bizarrely, one of what I shall say frames her from waist to knees...from behind. I'm not sure about that, perhaps it's being artistic. +John Baez gets some quotes in.

There are of course some strange things like saying Eugenia left a tenured professorship in Sheffield, which I guess is a transatlantic translation, when she still officially has a position there...
 
>> Dr. Cheng, 39, has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board. She is a theoretical mathematician who works in a rarefied field called category theory, which is so abstract that “even some pure mathematicians think it goes too far,” Dr. Cheng said. <<
It can also be a piece of pie, or custard — so says a professor and author who spreads the magic of numbers through dessert recipes.
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I asked some mathematics students, female and male, what they thought of the photo in question, and they all thought it really odd.
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Nice extra details not available on the (original) version in the book!

http://www.bodleian.ox.ac.uk/news/2016/may-03

#Tolkein  
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Very much so! Thank you, +David Roberts and +Kevin Clift 
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Anti-competition clauses in editor contracts

So while you can serve on other editorial boards, you cannot do anything the publisher deems as being competitive with their own journal. Like, I guess, start an open access journal on the same topic? This is why the research publishing system is monopolistic.

http://bjoern.brembs.net/2016/05/academic-publishers-and-competition/

(thanks to +Björn Brembs for writing this more eloquently than I could have)
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I actually think it's the other way around. If a publisher were solely doing the infrastructure, marketing, etc, of a product controlled and produced by the a particular scholarly community, then a clause like all emails to the publisher remains their property would be reasonable (because they'd likely only ever be commercial information). It's because the publishers control the whole thing that clauses like that are crazy. (I'm exmepting the overly broad "nothing considered detrimental to the journal in any way" clause, which is clearly overly broad.) That's one of the reasons competition won't work: it's trying to create more publishing entities but which again control too much of the process.
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Sci-hub data free to analyse

John Bohannon's recent article on Sci-hub is accompanied by a CC0-licensed dataset derived from the server logs of Sci-hub:

http://dx.doi.org/10.5061/dryad.q447c

There's also an IPython notebook used to do the analysis for the article, so you can check the results presented, or start to see what else can be done, if you are new to this.

#openscience
Title, Sci-Hub download data. Downloaded, 1060 times. Description, These data include 28 million download request events from the server logs of Sci-Hub from 1 September 2015 through 29 February 2016. The uncompressed 2.7 gigabytes of data are separated into 6 data files, one for each month, ...
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I live in Adelaide, Australia.

I am a pure mathematician who works on category theory and a smattering of related fields such foundations and higher geometry.

I am a visiting fellow in the School of Mathematical Sciences at the University of Adelaide.

My nLab page: http://ncatlab.org/nlab/show/David+Roberts
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