### Andres Caicedo

Shared publicly -I just gave a talk about writing a popular book on the Riemann Hypothesis: http://wstein.org/talks/2015-11-17-rh-book/slides/slides.pdf

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Andres Caicedo

Lives in Ann Arbor

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The below email is about the new mathematical research institute being set up in Melbourne. It is meant to be something like Banff/Oberwolfach/etc

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Most of you have by now heard about MATRIX, the new mathematical research institute based in Victoria. I would like to provide a bit of background about MATRIX, how it came to life and announce a new deadline for programs in 2017.

I think that researchers in the mathematical sciences consider it obvious that a dedicated institute improves quality and impact of research. A research institute has been a shared wish of many Australian mathematical scientists for a long time, yet despite several attempts over many years, Australia has remained one of the very few developed countries without such an institute.

In 2014 the momentum generated by the formation of the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) provided a rare and narrow window of opportunity which was too good to let pass, and so we went ahead. Instigated by ACEMS and by its Faculty of Science, The University of Melbourne decided in 2015 to put significant funding behind the formation of an international research institute in the mathematical sciences at a fixed venue in Victoria, called MATRIX. The aims of MATRIX are simple, to increase quality and impact of all Australian research in the mathematical sciences and to encourage interaction between mathematical and statistical researchers, whether they work in industry and/or academia.

Similar research institutes around the world each have a different modus operandi determined by the local context. After consultation with several colleagues we concluded that in the first years MATRIX programs should last between 2-6 weeks as this would work best in Australia. I expect around 20 residents present at any one time during a research program, but not necessarily the same 20 people each week. I also expect that MATRIX programs will usually contain a focus week in which a conference or embedded AMSI sponsored workshop may be held with a larger number of participants, and that programs of more than three weeks would include advanced-level short courses or a postgraduate lecture series.

MATRIX’ first call for activities in 2016 has recently closed and successful programs will be announced shortly. In 2016 these programs will take place at the Creswick campus, located in the heart of Victoria’s gold country and close to the popular getaways of Hepburn springs, Daylesford and Ballarat. We expect to run the first MATRIX program in June 2016.

MATRIX now invites prospective organisers to submit proposals for programs in 2017, the submission deadline is Friday 26 February 2016. Submission guidelines and further information can be obtained from http://www.matrixatmelbourne.org.au.

Programs submitted to MATRIX will be approved by the scientific committee of MATRIX whose members are selected to cover a wide range of expertise. The current committee members are Jan de Gier (UoM, Chair), Gary Froyland (UNSW), Liza Levine (Michigan), Kerrie Mengersen (QUT), Arun Ram (UoM), Joshua Ross (Adelaide), Terry Tao (UCLA) and Ole Warnaar (UQ).

MATRIX is fortunate to have a broad and strong Advisory Board chaired by Tony Guttmann (UoM). Current members of the board are Hélène Barcelo (MSRI), Peter Bouwknegt (ANU), Karen Day (UoM), Jan de Gier (UoM), Iain Johnstone (Stanford), Nalini Joshi (Sydney), Aleks Owczarek (UoM), Cheryl Praeger (UWA), Geoff Prince (AMSI), Brigitte Smith (GBS Venture Partners), Peter Taylor (UoM), Kari Vilonen (UoM) and Ruth Williams (UCSD).

We hope that the composition of the Scientific Committee and Advisory Board clearly demonstrates the intentions of MATRIX: to have a broad outlook and to be of benefit to the wider Australian mathematical sciences community. If you would like to know more about MATRIX, its mission or have queries about the submission guidelines, please contact me or our office staff Kate Hall or Lynne Williamson at office [ at ] matrixatmelbourne.org.au.

Jan de Gier

Director MATRIX

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Most of you have by now heard about MATRIX, the new mathematical research institute based in Victoria. I would like to provide a bit of background about MATRIX, how it came to life and announce a new deadline for programs in 2017.

I think that researchers in the mathematical sciences consider it obvious that a dedicated institute improves quality and impact of research. A research institute has been a shared wish of many Australian mathematical scientists for a long time, yet despite several attempts over many years, Australia has remained one of the very few developed countries without such an institute.

In 2014 the momentum generated by the formation of the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) provided a rare and narrow window of opportunity which was too good to let pass, and so we went ahead. Instigated by ACEMS and by its Faculty of Science, The University of Melbourne decided in 2015 to put significant funding behind the formation of an international research institute in the mathematical sciences at a fixed venue in Victoria, called MATRIX. The aims of MATRIX are simple, to increase quality and impact of all Australian research in the mathematical sciences and to encourage interaction between mathematical and statistical researchers, whether they work in industry and/or academia.

Similar research institutes around the world each have a different modus operandi determined by the local context. After consultation with several colleagues we concluded that in the first years MATRIX programs should last between 2-6 weeks as this would work best in Australia. I expect around 20 residents present at any one time during a research program, but not necessarily the same 20 people each week. I also expect that MATRIX programs will usually contain a focus week in which a conference or embedded AMSI sponsored workshop may be held with a larger number of participants, and that programs of more than three weeks would include advanced-level short courses or a postgraduate lecture series.

MATRIX’ first call for activities in 2016 has recently closed and successful programs will be announced shortly. In 2016 these programs will take place at the Creswick campus, located in the heart of Victoria’s gold country and close to the popular getaways of Hepburn springs, Daylesford and Ballarat. We expect to run the first MATRIX program in June 2016.

MATRIX now invites prospective organisers to submit proposals for programs in 2017, the submission deadline is Friday 26 February 2016. Submission guidelines and further information can be obtained from http://www.matrixatmelbourne.org.au.

Programs submitted to MATRIX will be approved by the scientific committee of MATRIX whose members are selected to cover a wide range of expertise. The current committee members are Jan de Gier (UoM, Chair), Gary Froyland (UNSW), Liza Levine (Michigan), Kerrie Mengersen (QUT), Arun Ram (UoM), Joshua Ross (Adelaide), Terry Tao (UCLA) and Ole Warnaar (UQ).

MATRIX is fortunate to have a broad and strong Advisory Board chaired by Tony Guttmann (UoM). Current members of the board are Hélène Barcelo (MSRI), Peter Bouwknegt (ANU), Karen Day (UoM), Jan de Gier (UoM), Iain Johnstone (Stanford), Nalini Joshi (Sydney), Aleks Owczarek (UoM), Cheryl Praeger (UWA), Geoff Prince (AMSI), Brigitte Smith (GBS Venture Partners), Peter Taylor (UoM), Kari Vilonen (UoM) and Ruth Williams (UCSD).

We hope that the composition of the Scientific Committee and Advisory Board clearly demonstrates the intentions of MATRIX: to have a broad outlook and to be of benefit to the wider Australian mathematical sciences community. If you would like to know more about MATRIX, its mission or have queries about the submission guidelines, please contact me or our office staff Kate Hall or Lynne Williamson at office [ at ] matrixatmelbourne.org.au.

Jan de Gier

Director MATRIX

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These are the notes from my colloquium talk yesterday at Vassar College. What a beautiful campus they have! And it was a pleasure to interact with the students and faculty there.

We didn't quite get a chance to cover everything in the notes during the talk.

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(No, I haven't seen http://blogs.ams.org/beyondreviews/files/2015/11/The-scary-place.jpg … They were all too scared to take Francisco or I the day he came for a tour of the building.)

What's the connection between MathSciNet and beer brewing? Mathematical Reviews Managing Editor Norm Richert satisfies our thirst for historical knowledge in his guest post on Beyond Reviews.

For the last 30 of its 75 years, the offices of Mathematical Reviews, housing roughly 78 staff members, have been in a red-brick building at 416 Fourth Street in Ann Arbor, Michigan. This building …

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Andres Caicedo

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Tim Gowers added the following comments, that of course G+ proceeded to remove here:

A new Polymath project has just started!

How many sets of size k do you need to choose in order to guarantee that there will be three sets A, B and C in your collection such that any point that lies in two of the sets lies in all three? (Equivalently, if you remove the points that belong to the intersection of all three sets, then the bits that are left are disjoint.)

Here's a proof that the bound is finite. That is, there is some n(k) such that if you have at least n(k) sets then they will include such a configuration.

First, pick a maximal disjoint subcollection of your sets. If it is of size at least 3 then you're done, so let's assume that you have either one or two sets in the subcollection. Let X be the union of the sets (so X has size either k or 2k).

Given any other set of size k, there are at most 2^{2k} intersections it can have with X. (We can obviously do better than this, but a crude estimate is OK for my purposes here -- I'm just using the fact that X has at most 2^{2k} subsets.) So if we have N sets not included in the union that made X, then we can find at least N/2^{2k} of them that have the same intersection with X. Also, this intersection is never empty, since otherwise we'd have a third disjoint set to add to our collection.

Let A be a collection of at least N/2^{2k} sets that all have the same intersection with X, and remove this common intersection from each of the sets of A. We now have a collection of sets of equal size, and that size is less than k. So by induction we can find in that configuration a collection of sets with the right property, and adding back in the common intersection with X we still have a collection of sets with the right property, and we're done (after checking that the base case is trivial, which it is).

This gives a bound of something like n(k) being at most 2^{2k}n(k-1), which gives an upper bound of 2^{Ck^2}. A better upper bound is known -- a fairly simple argument gives k!2^k. But what people would really like is an answer to the following question: is the correct upper bound exponential in k (the above bound having more of a k^k flavour)? This has been a famous open problem for a long time, and has fascinating connections with areas as apparently distant as the speed with which matrices can be multiplied together. One can (and does!) formulate the obvious generalization where one looks for r sets instead of 3.

Now Gil Kalai has started a Polymath project to see whether this problem can finally be cracked, or at least whether some progress can be made on it if a lot of people collaborate. I urge you to read his interesting initial post, and to contribute to the discussion. Remember that what is required from a Polymath comment is not a polished statement that looks as though it has been lifted out of a journal article. Anything constructive will do, such as a suggestion of a related question to think about, a reformulation of something that somebody else has said, an assessment of whether a certain approach is likely to work, or even just a comment saying, "I found what you wrote there interesting, but what exactly did you mean when you wrote X?" These small contributions have a way of adding up, until from time to time somebody suddenly makes a comment that changes the whole discussion.

I also recommend joining the discussion as soon as possible -- if only as a "lurker", since the longer you leave it, the harder it is to catch up. At the time of writing, it hasn't got going, so it's a good moment to read and digest Gil's initial post.

A new Polymath project has just started!

How many sets of size k do you need to choose in order to guarantee that there will be three sets A, B and C in your collection such that any point that lies in two of the sets lies in all three? (Equivalently, if you remove the points that belong to the intersection of all three sets, then the bits that are left are disjoint.)

Here's a proof that the bound is finite. That is, there is some n(k) such that if you have at least n(k) sets then they will include such a configuration.

First, pick a maximal disjoint subcollection of your sets. If it is of size at least 3 then you're done, so let's assume that you have either one or two sets in the subcollection. Let X be the union of the sets (so X has size either k or 2k).

Given any other set of size k, there are at most 2^{2k} intersections it can have with X. (We can obviously do better than this, but a crude estimate is OK for my purposes here -- I'm just using the fact that X has at most 2^{2k} subsets.) So if we have N sets not included in the union that made X, then we can find at least N/2^{2k} of them that have the same intersection with X. Also, this intersection is never empty, since otherwise we'd have a third disjoint set to add to our collection.

Let A be a collection of at least N/2^{2k} sets that all have the same intersection with X, and remove this common intersection from each of the sets of A. We now have a collection of sets of equal size, and that size is less than k. So by induction we can find in that configuration a collection of sets with the right property, and adding back in the common intersection with X we still have a collection of sets with the right property, and we're done (after checking that the base case is trivial, which it is).

This gives a bound of something like n(k) being at most 2^{2k}n(k-1), which gives an upper bound of 2^{Ck^2}. A better upper bound is known -- a fairly simple argument gives k!2^k. But what people would really like is an answer to the following question: is the correct upper bound exponential in k (the above bound having more of a k^k flavour)? This has been a famous open problem for a long time, and has fascinating connections with areas as apparently distant as the speed with which matrices can be multiplied together. One can (and does!) formulate the obvious generalization where one looks for r sets instead of 3.

Now Gil Kalai has started a Polymath project to see whether this problem can finally be cracked, or at least whether some progress can be made on it if a lot of people collaborate. I urge you to read his interesting initial post, and to contribute to the discussion. Remember that what is required from a Polymath comment is not a polished statement that looks as though it has been lifted out of a journal article. Anything constructive will do, such as a suggestion of a related question to think about, a reformulation of something that somebody else has said, an assessment of whether a certain approach is likely to work, or even just a comment saying, "I found what you wrote there interesting, but what exactly did you mean when you wrote X?" These small contributions have a way of adding up, until from time to time somebody suddenly makes a comment that changes the whole discussion.

I also recommend joining the discussion as soon as possible -- if only as a "lurker", since the longer you leave it, the harder it is to catch up. At the time of writing, it hasn't got going, so it's a good moment to read and digest Gil's initial post.

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Here's an idea from +Cory Doctorow, proposed in a series of tweets: "How to get every academic paper ever published into an open-access repository, in one easy step....Until a couple decades ago, virtually every university in America had work-for-hire arrangements with their faculty....These faculty, therefore, didn't hold the copyright they nominally assigned to the academic publishers over the past century....Thanks to copyright extension (not a phrase you'll see me type often!) we know that all those papers are still in copyright....Virtually everything behind academic publishers' paywall is therefore infringing, and subject to strict liability....Get one university, a Big 10 with sovereign immunity, to bring suit against the major academic publishers....The total damages would exceed the planet's total GDP several times over....The uni could limit itself to dead faculty without intact estates, so no risk of publishers suing the academics for indemnification....The university therefore offers to settle with the publishers: "Put everything in open access and we'll call it even."...To stir the pot, start by sending registered letters to the publishers' insurers, warning them that this is a potential liability...."

Cory and I talked about this briefly at last weekend's #F2i (Freedom to Innovate) conference at MIT <http://freedom2innovate.mit.edu/>. Among other things, I said I'd be surprised if a real-world court would invalidate all those past publishing contracts or find publishers guilty of mass infringement. But that was a prediction, not an objection. Courts could dismiss the idea even if legally sound, and we should not underestimate their tendency to protect incumbents. (Indeed, this was a theme of the #F2i conference.) But I added that I didn't think anyone had dived deeply into this idea to examine the legal merits or real-world obstacles. If I was right on the second point, then I hope someone will dive in. The idea deserves a closer look. If the analysis has been done or started somewhere, I hope someone can post links to the comment section.

BTW, many thanks to +Ethan Zuckerman for conceiving and organizing the #F2i conference.

#oa #openaccess #copyright #workforhire

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Overview Barry Mazur and I spent over a decade writing a popular math book "Prime Numbers and the Riemann Hypothesis", which will be published by Cambridge Univeristy Press in 2016. The book involves a large number of illustrations created using SageMath ,...

Overview Barry Mazur and I spent over a decade writing a popular math book "Prime Numbers and the Riemann Hypothesis", which will be published by Cambridge Univeristy Press in 2016. The book involves a large number of illust...

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For anyone who would like to know more about Laci Babai's talk yesterday on the graph isomorphism problem, it was livetweeted by Gabriel Gaster, who has done us unfortunates who don't live in Chicago a great service. Although obviously he couldn't tweet an entire proof, one can extract a surprisingly large amount of information (and better still, in a very short time) from his tweets about what the proof is like. In particular, it seems that the broad structure of the proof is a divide-and-conquer algorithm that deals with most graphs, but reduces the problem to looking at some particularly troublesome examples called Johnson graphs. But the latter can be understood sufficiently precisely that they can be dealt with algebraically (using the classification of finite simple groups). Also, while Babai's algorithm is a stunning theoretical advance, it won't be challenging the algorithms that are used in practice. Here the situation is similar to that with primality testing, where despite the existence of a polynomial-time deterministic algorithm, a randomized algorithm is more practical to use if you actually want to test whether a number is prime.

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I've just received the sad news that Klaus Roth has died. He is best known for his remarkable result that algebraic numbers are hard to approximate by rationals. Liouville's theorem states that if x is an irrational solution of a polynomial of degree d (with integer coefficients), then there is a constant c such that |x-p/q| is at least c/q^d for every pair of integers p and q. Roth showed that you can replace d by any power greater than 2. That is, if alpha>2, then there is a constant c such that the bound can be replaced by c/q^alpha.

Another famous result of his, which has had a huge influence on my mathematical life, is his proof of the first non-trivial case of Szemerédi's theorem: that for every delta there exists n such that every subset of {1,2,...,n} of size at least delta n contains an arithmetic progression of length 3.

Although he had rather withdrawn from the mathematical community in his last years (he was 90), he will be sorely missed.

Another famous result of his, which has had a huge influence on my mathematical life, is his proof of the first non-trivial case of Szemerédi's theorem: that for every delta there exists n such that every subset of {1,2,...,n} of size at least delta n contains an arithmetic progression of length 3.

Although he had rather withdrawn from the mathematical community in his last years (he was 90), he will be sorely missed.

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#science #awards

Science is starting to pay big for a small minority who land major prizes. At a ceremony in California on Sunday night, six researchers became substantially wealthier when they were handed Breakthrough prizes, set up by the Russian billionaire Yuri Milner along with some of the biggest names in Silicon Valley.

Among those honoured were Karl Deisseroth of Stanford University and Edward Boyden of MIT for developing a procedure called optogenetics – a means of turning neurons on and off using light. They took home $3m (£2m) apiece for winning the Breakthrough prize in life sciences.

The same prize winnings went to John Hardy, who studies Alzheimer’s disease at University College London; Helen Hobbs, of the University of Texas South-western medical centre, for discovering gene variants linked to cholesterol;Svante Pääbo at the Max Planck Institute for Evolutionary Anthropology in Leipzig for reading Neanderthal and other ancient genomes; and Ian Agol, a mathematician at the Institute for Advanced Study in Princeton, for his work on problems that language cannot easily convey: virtual Haken, virtual fibering conjectures and tameness.

Science is starting to pay big for a small minority who land major prizes. At a ceremony in California on Sunday night, six researchers became substantially wealthier when they were handed Breakthrough prizes, set up by the Russian billionaire Yuri Milner along with some of the biggest names in Silicon Valley.

Among those honoured were Karl Deisseroth of Stanford University and Edward Boyden of MIT for developing a procedure called optogenetics – a means of turning neurons on and off using light. They took home $3m (£2m) apiece for winning the Breakthrough prize in life sciences.

The same prize winnings went to John Hardy, who studies Alzheimer’s disease at University College London; Helen Hobbs, of the University of Texas South-western medical centre, for discovering gene variants linked to cholesterol;Svante Pääbo at the Max Planck Institute for Evolutionary Anthropology in Leipzig for reading Neanderthal and other ancient genomes; and Ian Agol, a mathematician at the Institute for Advanced Study in Princeton, for his work on problems that language cannot easily convey: virtual Haken, virtual fibering conjectures and tameness.

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As rumors go, this (quasipolynomial time for graph isomorphism, improving Babai and Luks 1983 exponential in the square root of n) seems like a pretty big one.

Next Tuesday, a week from today, Laci Babai will talk at the University of Chicago about a new algorithm that solves graph isomorphism in quasipolynomial time. There should also be a follow-up talk...

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A blog-post marking the sad death of a friend and colleague.

http://richardelwes.co.uk/2015/10/28/barry-cooper-1943-2015/

Barry Cooper, who very sadly died on Monday, was a central member of the Leeds logic group since the 1960s. I joined that group as a graduate student in 2001, and since then have had the pleasure t...

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Mathematician. Associate editor at Math Reviews. Father of two.

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