New app on Play Store: G(n,p) random graphs!
Seasoned readers of this blog already know the ins and outs of the Erdős–Rényi random graph model. They have probably read the introductory blogpost, have doodled and ruminated about them in class, and...
View ArticleFranck, frankly
If you want to listen to something while reading this post, you can listen to this recording of Franck’s violin sonata. If asked, I would not say that César Franck is my favorite composer. I remember...
View ArticleFour remarks on citations
1. There is a very special level of hell. A level they reserve for people who write, “This type of result can be extended to higher dimensions, see e.g. [reference1]”, where [reference1] is a 300 page...
View ArticleThe simplest hyperbolic doughnut
In my current research, I study hyperbolic surfaces; these are surfaces where every point locally has the geometry of the hyperbolic plane. In this post, we will talk a bit about hyperbolic geometry,...
View ArticleThe useful inequalities cheat-sheet
It has recently come to my attention that not every living being in the world knows the famous “Useful Inequalities” cheat-sheet, produced by László Kozma and available from his website (or here for a...
View ArticleThe useful Weierstrass inequality
This is post #1 in the series about the “Useful Inequalities” cheat-sheet. Today’s useful inequality: The Weierstrass inequality. In its most basic form (simpler than what appears in the cheat-sheet),...
View ArticleYou only need one
Oh! The places you’ll go! You’ll be on your way up!You’ll be seeing great sights!You’ll join the high flierswho soar to high heights. You won’t lag behind, because you’ll have the speed.You’ll pass the...
View ArticleThe useful Chebyshev sum inequality
This is post #2 in the series about the “Useful Inequalities” cheat-sheet. Today’s useful inequality: Chebyshev’s sum inequality. Almost everyone I know is familiar with the famous Chebyshev’s...
View ArticleThe useful Paley-Zygmund inequality
This is post #3 in the series about the “Useful Inequalities” cheat-sheet. Today’s inequality: The Paley-Zygmund inequality. A large portion of probability theory involves showing that random variables...
View ArticleHow convenient!
It’s 07:00 in the morning. Having just gotten out of bed, you already poured yourself some breakfast cereal into the bowl, when you come to the most horrifying realization: you’re fresh out of milk....
View ArticleNew paper on arXiv: A sharp lower bound on the eigenvalues of surfaces
I’m happy to say that my postdoc advisor Asaf Nachmias, his student Guy Lachman and I have recently uploaded a paper to the arXiv under the title “A sharp lower bound on the eigenvalues of surfaces”...
View ArticleThe seasons
When I was a kid, I learned about the seasons. Autumn, winter, spring, and summer, repeating in an endless cycle. Autumn, I must admit, I didn’t much notice. But in winter it rained, and sometimes...
View ArticleG(n,p) does not decay
A well-used door needs no oil on its hinges.A swift-flowing stream does not grow stagnant.A deer blends perfectly into the forest colors.Software rots if not used. These are great mysteries. The Tao of...
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