## The canonical model structure on CatNovember 16, 2012

Posted by Chris Schommer-Pries in Algebraic Topology, Category Theory.

In this post I want to describe the following result, which I think is pretty neat and should be more widely known:

Theorem: On the category of (small) categories there is a unique model structure in which the weak equivalences are the equivalences of categories.

## Shameless conference promotionNovember 14, 2012

Posted by Ben Webster in Uncategorized.

So, obviously posting on this blog has ebbed a little (I keep hoping to reverse this trend, but I think we’ve all found that demands on our time that come before blog posting tend to ratchet upward, not downward).  I assume there are still a few people reading, though, and I wanted to do a little promotion.

One of the thing that’s been demanding my time lately has been conference organization.  We’re planning a conference at Northeastern next spring in recognition of the 60th birthday of Andrei Zelevinsky, with the exteremely original name of “Algebra, Combinatorics and Representation Theory”. I think it’s going to be great, and I encourage any of you who are able and interested to attend; we have a really great line-up of speakers.

For more information, see our website.  I want to particularly encourage young people to attend; we’re really hoping (cross your fingers) to have funding for grad students and postdocs.  (Furthermore, it will help us to obtain said funding if young people express an interest in coming.  So, if you would like to come, please register).

## Rant to me about algebra booksOctober 25, 2012

Posted by David Speyer in Uncategorized.

Next term, I will be teaching the second semester of graduate algebra here at Michigan. The big mandatory topics are finite groups and Galois theory. There is usually time for a bit more of whatever the instructor wants to fit in. I want to do some representation theory. In my dreams, we’ll also do a bit of playing with number fields, but that might be overly ambitious.

My project for the next few weekends is to skim through as many algebra texts as I can and pick one to use. So I thought I’d put up a request for your opinions. Below the fold, some of my criteria:

## What I’m readingOctober 24, 2012

Posted by David Speyer in Uncategorized.

I haven’t had a long post for a while, but there is lots of great math on the internet. Here are some of the things I’m trying to find time to read.

Integrable systems, toric geometry and Okounkov bodies The answer to a question which many people have asked: What’s the relationship between integrable systems and torus actions? Allen Knutson has been telling people roughly what the picture should be for a while, but the details seemed very hairy; now they are all resolved. That gets us half way to the question I want to know the answer to: “What is the relation between these integrable systems and cluster algebras?”

A closed formula for the decomposition of tensor products of Specht modules for the symmetric group A positive formula for stable Kronecker coefficients! (Corollary 4.08) And a proof which relies on the sort of planar diagram philosophy that people on this blog love. Congratulations to Bowman, de Visscher and Orellana.

Causal diagrams and causal models Not new, but new to me. I had always learned that, if $X$ and $Y$ are correlated, then the only way to tell which one causes which (or whether they are both caused by something else) was by a randomized trial. Not true! You can make this determination in a purely observational manner, by seeing how $X$ and $Y$ both correlate with $Z$. Apparently, this was known since the late 80′s, but my stats course never covered it. Makes me want to go back and work in algebraic statistics.

And I’ll take the opportunity to plug a paper of my own which has been a long time coming. Schubert problems with respect to osculating flags of stable rational curves The Shapiro-Shapiro conjecture, now proved by Mukhin, Tarasov and Varchenko shows that any $N$ distinct points on $\mathbb{RP}^1$ give Schubert problems whose solutions are, astonishingly all real. What happens when the points collide? And what does this have to do with the work of Henriques and Kamnitzer?

## It would be harmful to design all mathematical contests to be proctorableSeptember 30, 2012

Posted by David Speyer in Uncategorized.

This rant is inspired by a debate going on at meta.math.SE. The subject of the debate is what steps the moderators should take to prevent the use of math.SE to cheat in ongoing math competitions. If you have an interest in the subject and an account on meta.math.SE, I encourage you to head over and participate including, if you are so inclined, voting on the poll questions I just posted.

The particular point I want to address is posters who write that the fault is with contest organizers, for not designing their contests with internet age security in mind. A typical exemplar of this viewpoint writes

[Cheating] is a problem with folks using antiquated methods for tests, contests, etc. – methods that are a poor fit to the current information age. Any problems they encounter should be fixed at the source – not kludged here.

I strongly disagree.

## Michigan panel on math teaching in the age of internet forumsSeptember 28, 2012

Posted by David Speyer in Uncategorized.

Sorry for disrupting non-Michigan people with this, but on Monday Oct. 1, at 5:40 PM, I will be on a panel in East Hall B844 on teaching math in the age of google and math.SE. I haven’t been given a list of topics, but I’m hoping to talk about both how to do accurate evaluation of our own students, and how to ethically help other institutions’ students. All levels of participant, from undergraduate up to full professor, are welcome to attend. I assume there will be an official announcement going out, but I thought people interested in the topic might see it better here.

## Bill Thurston 1946-2012August 23, 2012

Posted by David Speyer in Uncategorized.

Bill Thurston died on the evening of August 21st. His son Dylan writes “He was surrounded by family, and went very peacefully, after a fight with melanoma since spring 2011. Please pass this on as appropriate.”

I knew Professor Thurston only through his writing, first in publication and recently on Mathoverflow. It was always a joy. I have avoided more routine obligations than I care to admit by reading and rereading his papers. He believed that mathematics was a fundamentally human task, and that his goal was not simply to provide the reader with a bulleted list of truths, but to provide a picture and an intuition that made them obvious.

I had the thought to organize a blogfest, where various math bloggers would write up expositions of some aspect of his work. But I ran into an obstacle: What subject did I think I could explain better than he did? So, instead, here are some of my favorites, for your pleasure and inspiration:
(more…)

## Quick Mathematica squibAugust 14, 2012

Posted by David Speyer in Uncategorized.

I have spent a lot of time manipulating multivariate polynomials in Mathematica, and have been very frustrated at trying to make Coefficient behave the way I think it should. I think Coefficient[2x+3xy, x] should be 2, Mathematica thinks it should be 2+3y. Or rather, I don’t think that this should be the default, but it is very often my desired behavior and I can’t find an option to tell Mathematica that’s what I want.

I just wrote a little snippet to do this for me, and I’m copying it here so I can reuse it in the future:

myCoeff[poly_, vars_, exp_] :=      If[Max[exp] == 0, poly, Coefficient[poly, Apply[Times, vars^exp]]] /.        Map[(# -> 0) &, vars]

For example, myCoeff[2 x + 3 x*y, {x, y}, {1, 0}] is 2, just as I want. Note that myCoeff[2k*x+2x*y, {x,y}, {1,0}] is 2k; so you can still easily have Mathematica treat some variables as constants.

UPDATE Code simplified a bit, because I realized that creating useless replacement rules wouldn’t do any harm.

## El Naschie loses libel suit against NatureJuly 11, 2012

Posted by David Speyer in Uncategorized.

A British court has just ruled against Mohammed El Naschie in his libel case against Nature. To quote from the decision:

My conclusions are that the article is substantially true … and that it was the product of responsible journalism.

To my mind, this basically finishes the story of El Naschie the man, but does not conclude the question of how such a journal was allowed to remain at Elsevier for so long.

Past El Naschie threads have been unpleasant and unproductive, so I’m leaving comments closed on this one. Thanks to Mike Usher at Math 2.0 for making me aware of this news.

## Why aren’t my prime pictures pretty?July 3, 2012

Posted by David Speyer in Uncategorized.
This is a followup to my post What if primes hated to start with nine? and you might want to read that post for context. This post describes my failure to create a nice illustration of the effect of the zero of $\zeta$ at $1/2 + 14.134725 i$ on the distribution of the primes. Of course, the answer might be really dumb — I might just have a coding error, or the range of primes I was using (around $10^9$) may not be large enough. But I suspect there is something interesting here, and I’d like to know what. The basic question of this post is “Why does the left hand graph look as random as the right hand one?”