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
The Technion offers many of its mathematics courses, such as infinitesimal calculus and algebra, at several levels, with each course aimed at a different audience. At the lowest level are courses aimed at the “soft sciences”, such as biology, which usually need only elementary, practical calculations. In the middle sit the majority of the Technion’s … More Introduction to sandwich making
My wife has (repeatedly) brought to my attention the following two facts: Of the 135+ posts on this blog, none is about cats (I guess that this complex transformation post doesn’t really count). This blog is on the internet. A glaring omission if ever there was one, and not one easily forgiven. So today I’d … More Kot Theodore
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 just got back from Paris, where I participated in a summer school on high dimensional probability and algorithms. This was a cool school, with a course on mirror descent by Sébastien Bubeck and a course on applications of matrix sampling by Joel Tropp. I might even get to write about the mathematical content one … More People of Paris
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
I’m happy to say that I recently uploaded a paper to the arXiv under the title “A conformal Skorokhod embedding” (https://arxiv.org/abs/1905.00852). In this post, I’d like to explain what the Skorokhod embedding problem is, how I came across it, some previously known solutions, and my own tiny contribution. But really, all of this is just … More New paper on arXiv: A conformal Skorokhod embedding
A sole soul in a sole, travelling. Where did it come from? Where will it go?There are things that humankind is not meant to know.
Part 1: Archery Lately I’ve been interested in archery. The target of target archery is to shoot a circle square in the middle. The target is usually placed quite far away, some 70 meters in the case of the Olympic games, so it’s not always very easy. Here is one of my volleys from 18 … More Low-dimensional archers have it easy
Here is a silly little question that my friend Ori and I ran into. Let be a decreasing sequence of positive real numbers which tends to 0. Perhaps in a more decent universe, the sum would always equal some finite number, but already in kindergarten we learn that that’s not true: For example, the partial … More Converging Bernoulli Series
Still probably the best 70$ I ever spent.
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!
Here is a neat question that I stumbled upon during my academic random walk. A sequence of vectors is called an arithmetic progression of length k if there exists a vector such that . In other words, an arithmetic progression in is exactly the generalization you would expect of your good ol’ high-school arithmetic progression … More Arithmetic progressions in space?