“TeX, LaTeX and Friends” StackExchange site also looking for people June 22, 2010
Posted by Ben Webster in Uncategorized.13 comments
As those of you who follow StackExchange drama know (StackExchange is the platform that MathOverflow runs on), there was recently a change in how StackExchange sites are set up. Unlike the situation when MO was born, when anyone with a dream and willingness to pay cash could start a site, now they go through a process to ensure that there is community support. The stage of this process before beta is to get people to commit to using the site to show that the community has enough support.
There’s a proposal for a Q & A site on (La)TeX which has now entered this stage and needs supporters to be launched. I think such a site would be an amazing resource for mathematicians (and others, of course), and I really want to see it launched. If you agree and want to sign up, go here.
Statistics version of MathOverflow looking for beta testers June 17, 2010
Posted by David Speyer in Uncategorized.21 comments
Rob Hyndman is trying to start a question and answer site for people working in Statistics, running on the same software system that supports our beloved MathOverflow. Due to a change in the way StackExchange is licensing their platform, he can’t simply get up and start using it. Rather, he must first obtain a critical number of users who will commit to regularly checking in and using the site. If you would be interested and capable of making this commitment, head on over to Statistical Analysis — Area 51. I find the new policy strange, but that’s apparently how things are working now.
I think that a Statistics version of MathOverflow would be a great idea. All the time, people come to me or to MathOverflow asking questions that are really meant for a statistician. There are a lot of sophisticated questions in Statistics, and it would be good to have a place for them to be answered.
I also think it would be good for us mathematicians to check in more on what the statisticians are doing. Great math has often been driven by the needs of the other sciences; and one of the big needs of today is for better methods for analyzing large data collections. I can say that my advisor, Bernd Sturmfels, has found a lot of pretty algebraic geometry problems by trying to help out our local statisticians.
Disclaimer: I don’t know Professor Hyndman, and have no involvement with this project other than wanting it to succeed.
Some questions about motives June 13, 2010
Posted by David Speyer in Algebraic Geometry.4 comments
As I tried to read up on motives in preparation for my last post, I thought of some questions that seemed natural to me, but weren’t addressed in the sources I was reading. So here they are, in the hope that experts will find them obvious. One set of questions concerns motives for nonproper varieties, the other concerns higher categorification.
Things I just noticed June 11, 2010
Posted by David Speyer in Uncategorized.13 comments
Euclid famously said “There is no Royal Road to Geometry.” But if you want to get to the American Institute of Mathematics in Palo Alto, guess what you drive along?
Motive-ating the Weil Conjecture Proof June 10, 2010
Posted by David Speyer in Algebraic Geometry, Category Theory.add a comment
This post concludes a series of posts I’ve been writing on the attempt to prove the Weil Conjectures through the Standard Conjectures. (Parts 1, 2, 3, 4, 5.) In this post, I want to explain the idea of the category of motives. In the modern formulation of algebraic topology, cohomology theories are functors from some category of spaces to the category of abelian groups. The category of motives is meant to be a universal category through which any such functor should factor, when the source space is the category of algebraic varieties. At least in the early days of the subject, the gold test of this theory was the question of whether the Weil Conjectures could be proved entirely in this universal setting. Nowadays, this question is still open, but the use of motives has grown. To my limited understanding, this growth has two reasons: among number theorists, it has become clear that motivic language is an excellent way to formulate results on Galois representation theory; among birational geometers and string theorists, many applications have been found for motivic integration. There will be a bunch of category theory in this post, which I hope will make it more attractive to the tensor category crowd.
I am much less comfortable with this topic than the other posts in this series; my understanding doesn’t go much further than Milne’s survey article. So I’m going to make this post a pretty short introduction to the main ideas. That will be the end of my expository posts; I also want to write one more post raising some questions about motives that seem natural to me.
