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Factoring With Bicycle Chains

As penance for teasing you on April Fool’s Day, I have another exercise on factoring. Today we will simulate a machine invented by Derrick H Lehmer (the son of the famous father-son-daughter-in-law trio of mathematicians named Lehmer) that uses bicycle chains to factor integers. Unlike the previous exercise, this factoring method is real; in fact, […]

Finite time blowup for an averaged three-dimensional Navier-Stokes equation

I’ve just uploaded to the arXiv the paper “Finite time blowup for an averaged three-dimensional Navier-Stokes equation“, submitted to J. Amer. Math. Soc.. The main purpose of this paper is to formalise the “supercriticality barrier” for the global regularity problem for the Navier-Stokes equation, which roughly speaking asserts that it is not possible to establish […]

The many stages of writing a paper, and how to close the deal.

[tl;dr] Producing a piece of research for publication has many stages, and each stage has different needs, requiring different ways of operating. Learning these stages is a key developmental step for a graduate student. In what follows,...Show More Summary

FOCS Reception sing-along

Tomorrow night at 7:30 (before the FOCS business meeting at 9), the Positive Eigenvalues will be playing a live set for the entertainment of FOCSers. Who are the Positive Eigenvalues, you might ask ? Well, you'll have to come and hear us to find out :). Show More Summary

Life at Simons

There have been many posts on the technical talks happening at Simons (see +Moritz Hardt's latest on gradient descent if you haven't yet). Not as many yet on the less-formed discussions that are happening in and around the building,Show More Summary

Conference videos

Well, from my perspective at least, the conference was a success.  We all made it through in one piece, and no one got trapped on the subway. If any of you are looking for the videos of the talks, they can be downloaded from this page. That’s a only a temporary hosting solution, but at [...]

The Great Race

This post is by Phil. Last summer my wife and took a 3.5-month vacation that included a wide range of activities. When I got back, people would ask “what were the highlights or your trip?”, and I was somewhat at a loss: we had done so many things that were so different, many of which [...]

Seminar on the Cobordism Hypothesis and (Infinity,n)-Categories

Well, it’s been a while, but it’s now a new semester here in Hamburg, and I wanted to go back and look at some of what we talked about in last semester’s research seminar. This semester, Susama Agarwala and I are sharing the teaching in a topics class on “Category Theory for Geometry“, in which [...]

Chomsky chomsky chomsky chomsky furiously

Noam Chomsky elicits a lot of emotional reactions. I’ve talked with some linguists who think Chomsky’s been a real roadblock to research in recent decades. Other linguists love Chomsky, but I think they’re the kind of linguists I wouldn’t spend much time talking with. Many people admire Chomsky’s political activism, but sociologist blogger Fabio Rojas [...]

No one knows what it’s like to be the bad man

Part 1. The ideal policy Basbøll, as always, gets right to the point: Andrew Gelman is not the plagiarism police because there is no such thing as the plagiarism police. But, he continues: There is, at any self-respecting university and any self-respecting academic journal, a plagiarism policy, and there sure as hell is a “morality” [...]

A pictorial proof of the hairy ball theorem

The hairy-ball theorem says that there is no continuous non-zero vector field on the surface of a sphere. There are lots of popular accounts that tell you what this means, giving great examples. Here's a Youtube video for example: My...Show More Summary

“If our product is harmful . . . we’ll stop making it.”

After our discussion of the sad case of Darrell Huff, the celebrated “How to Lie with Statistics” guy who had a lucrative side career disparaging the link between smoking and cancer, I was motivated to follow John Mashey’s recommendation and read the book, Golden Holocaust: Origins of the Cigarette Catastrophe and the Case for Abolition, [...]

Algebraic twists of modular forms, III

After a small break while traveling, I continue the discussion of my paper with Fouvry and Michel, continuing from here. But first of all, I’m happy to mention two proofs of the counting identities mentioned in my introductory post: one that D. Zywina has sent me, a nice proof based on explicit computations of modular [...]

Guest Post: Report from the Snowbird Math Research Communities program

My student Amirali Abdullah attended a recent MRC event on discrete and computational geometry at Snowbird, organized by Satyen Devadoss, Vida Dujmovic, Joe O'Rourke, and Yusu Wang. This is his (lightly edited) report from the event....Show More Summary


I bought this book in the Zürich Kunsthaus shop before even realizing that the cover was an example of an Apollonian circle packing. Statically, this doesn’t look like much. But with the proper tool, it moves… (click on the picture to get the movie; more examples here..) The author is Takahiro Kurashima, and the publisher [...]

Multiplicative Weight Updates as Zombie Binary Search

The multiplicative weight update method (MWU hereafter) is a neat algorithm design technique with applications in machine learning, geometry and optimization among others. However, it's viewed (and discussed) as an advanced technique,...Show More Summary

STOC 2012 Posters: Submit your abstract now !

As I mentioned earlier, STOC 2012 is repeating the successful poster event from STOC 2011. For more details on the logistics of submitting, see my post. What I'd like to do is give you more reasons to submit ! No one attends talks ! Ok,...Show More Summary

A Cheerier Link

I was told that the last two posts — on Hitler and serial killers — were too depressing, and that I need to post something more cheery So here is a careful analysis of the physics of My Little Pony.

Hitler on Topology

At this point, I’m sure everyone has seen at least one of the YouTube videos of Hitler ranting (actually actor Bruno Ganz from the movie Downfall) with fake subtitles. Here’s one showing Hitler’s reaction to discovering that in topology a … Continue reading ?

Wind and Mr. Ug

You should watch Vi Hart's stop-motion animated story of Wind and Mr. Ug.

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