Discrepancy, Graphs, and the Kadison-Singer Problem

Discrepancy theory seeks to understand how well a continuous object can be approximated by a discrete one, with respect to some measure of uniformity. For instance, a celebrated result due to Joel Spencer says that given any set family $latex {S_1,\ldots,S_n\subset [n]}&fg=000000$, it is possible to color the elements of $latex {[n]}&fg=000000$ Red and Blue … Continue reading Discrepancy, Graphs, and the Kadison-Singer Problem

Reasons to care: In honor of Scott Aaronson

Update (5/7): This post earned me a spot on the not-so-exclusive club of people called names such as a "narrow-minded" "biased" "religious worshiper" "who  doesn't want to learn something difficult and new" by Luboš Motl. Interestingly, he mostly takes issue with my discounting the possibility that the complexity of SAT is something like $latex n^{1000}$ or $latex … Continue reading Reasons to care: In honor of Scott Aaronson