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, investigate various hyperbolic surfaces, answer the question “what is the simplest hyperbolic doughnut”, and see why it is actually a pretzel. More … More The simplest hyperbolic doughnut
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 book. How difficult could it have been to cite a specific theorem? a page number? A section? a chapter? … More Four remarks on citations
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 have dreamt about them frequently, if not constantly. But until now, they have not had the pleasure of sharing their fresh-from-the-oven random … More New app on Play Store: G(n,p) random graphs!
Over the past thousand years, I’ve been working on setting up a shared online wiki called the Boolean Zoo (https://booleanzoo.weizmann.ac.il/index.php/Main_Page). The point of the wiki is to collect lots of different examples of Boolean functions, together with pretty much all the properties that are known about them. Each function has a page containing a short … More The Boolean Zoo
Disclaimer: I first of all want to say that it’s perfectly, perfectly normal to think about these issues. Trust me, I have a dog. Garbage collection is no joke, and no amount of algorithms is too great when planning where to put the next bin. For several years now, I have proudly called myself the … More Garbage planning
In case the previous post concerning concentration on the Boolean hypercube wasn’t enough for you, you can now watch a short, 20-minute animated video that I made for the STOC 2020 conference in theoretical computer science: STOC is a large (by theoretical computer science standards anyway) annual conference, which was supposed to take place in … More STOC 2020 lecture available online
I’m happy to say that the paper “A phase diagram for bacterial swarming” has been published in Communication Physics (https://www.nature.com/articles/s42005-020-0327-1). This paper is the result of ancient long-running research (started in 2015…) and is joint work with Avraham Be’er, Bella Ilkanaiv, Daniel Kearns, Sebastian Heidenreich, Markus Bär and Gil Ariel. In it, we analyze how … More New paper in Communication Physics: A phase diagram for bacterial swarming
I’m happy to say that my advisor Ronen Eldan and I somewhat recently uploaded a paper to the arXiv under the title “Concentration on the Boolean hypercube via pathwise stochastic analysis” (https://arxiv.org/abs/1909.12067), wherein we prove inequalities on the Boolean hypercube using a cool continuous-time random process. In the previous post, I pretended that I had … More New paper on arXiv: Concentration on the Boolean hypercube via pathwise stochastic analysis
I’m happy to say that my advisor Ronen Eldan and I somewhat recently uploaded a paper to the arXiv under the title “Concentration on the Boolean hypercube via pathwise stochastic analysis” (https://arxiv.org/abs/1909.12067), wherein we prove inequalities on the Boolean hypercube using a cool continuous-time random process. That’s quite a mouthful, I know, and quite unfortunately, … More Catastrophic cubic crash course
This post is about the basics of the “gradient descent” method for finding the minimum of a function. I started writing it mainly to review the optimization material of lectures by Sébastien Bubeck given in Seattle. All of the material can be found elsewhere (for example, Sébastien’s book), but I can assure you that in … More Descent into madness
I recently stumbled across a nice word game called “Doublets”, invented by Lewis Carroll. It goes like this. Player 1 writes two words with the same number of letters, say “cone” and “hoof”. Player 2 must then find a chain of words, each of them differing by one letter, which starts at the first word … More Doublets: From amok to updo in 14 easy steps
Last time I introduced a neat little question: Is it true that every infinite path in contains arbitrarily long arithmetic progressions? For example, in the following path, the squares colored in red have coordinates , which form an arithmetic progression of length 3, where every two consecutive points differ by . As it turns out, … More Arithmetic progressions in space!
Dedicated to Harold Cohen, who died last year, and to his son AARON. I Grunting softly, the father slipped out of bed. The mother stirred the faintest amount, her shoulders sliding a sliver of a hair, noticing the sudden emptiness besides her. But her breathing kept its pace, and she remained in gentle slumber. No … More Three scenes from childhood
At the end of the semester, in order to see their grades, students at the Weizmann Institute must complete an online survey about each course they participated in. The survey asks questions about both the course and the teachers, and the results are then shown in a “previously, on ‘Topics in Holomorphy’ ”-styled section in … More Few courses are better
My piano is mentally ill. Now, you might be wondering how it is that a piano can be sick, but it’s an electronic piano (Korg SP250), and thus has a specialized electronic brain in charge of imitating the sound of tiny hammers hitting strings when I press its plastic keyboard. And like any brain, it … More Electric Insanity
My wife and I have a problem. Well, I mean, not a problem, per se. We are “of divided opinions”. She wants to have a baby. I want to program. The two are obviously incompatible. And it’s not that she doesn’t like to program, she loves it very much, coding away her will and command; … More Skin and bits
Sarcastic Resonance 