Holla!

My math sibling Anton Dochtermann recently posted a paper to the Arxiv, HOM COMPLEXES AND HOMOTOPY THEORY IN THE CATEGORY OF GRAPHS introducing the idea of weak equivalence to the category of graphs (model graph category anyone?) and subsumes other graph homotopy theories into the framework. This is all a natural progression of research that has its roots in in the topological ideas introduced in Lov’asz’s proof of Kneser’s conjecture and culminates in K-theory for graphs I suppose.

Stay tuned for a paper from another math sibling Matt Kahle, giving classes of graphs for which the chromatic number estimate in Lov’asz’s proof is tight.

Mathematics into the Twenty-First Century

Eagle-eyed Peter Woit spotted an interesting volume on AMS Books Online: a collection of survey articles called Mathematics into the Twenty-First Century. The papers were originally presented at a conference in 1988 held in honor of the AMS’ 100th anniversary. Collectively they provide a picture of the frontier of mathematical research.

AMS Books Online has also added a three-volume history of American mathematics to its General interest section.

Spam

I’ve just deleted about 200-300 spam comments that have appeared over the last day or two.  I don’t think I accidentially deleted any actual comments, but if I did, please post again.

Trackbacks (and pingbacks) have now been disabled so there shouldn’t be any more spam and the comment RSS feeds should (hopefully) be safe to subscribe to again.  I’d like to re-enable trackbacks again at some stage, but probably not until I’ve figured out how to block this bulk spam.

Easwaran on Conditional Probability

Frequent commenter Kenny Easwaran (who also has a weblog, Antimeta, devoted to philosophy of math) has written several interesting essays on the interpretation of conditional probability:

The question is practically and philosophically interesting in the case that the event you are conditioning on occurs with probability zero.

Saul Kripke

I wanted to give the philosphers in our audience a chance to patronize me for my ignorance. I had no idea until the past few days that Saul Kripke is an important and widely influential philosopher. I knew him from his work in modal logic, but I imagined that he was a logician who worked on a technical subject on the margins of philosophy. (At least I’m better informed than a guy I know who assumed that Kripke must be a category theorist, because there’s something called Kripke-Joyal semantics, which is a translation of Kripke’s work into the language of topos theory.)