Lecture 7 First passage percolation 1) Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in ndimensional space. (Other graphs were considered later as … Continue reading →
Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of FourierWalsh expansion of Boolean functions and the use of Hypercontractivity. Before that we started with a very nice discrete isoperimetric question on a … Continue reading →
Borsuk asked in 1933 if every bounded set K of diameter 1 in can be covered by d+1 sets of smaller diameter. A positive answer was referred to as the “Borsuk Conjecture,” and it was disproved by Jeff Kahn and me in 1993. … Continue reading →
Home page of the course. In the first lecture I defined the discrete ndimensional cube and Boolean functions. Then I moved to discuss five problems in extremal combinatorics dealing with intersecting families of sets. 1) The largest possible intersecting family … Continue reading →
After much hesitation, I decided to share with you the videos of my lecture: Open collaborative mathematics over the internet – three examples, that I gave last January in Doron Zeilberger’s seminar at Rutgers on experimental mathematics. Parts of the 47minutes … Continue reading →
This fall I am giving a course at Berkeley on analysis of Boolean functions Course number: CS 29492 Title: Analysis of Boolean Functions Lectures: TuTh 5:006:30 Location: Room 310 Soda First lecture will be was on Thursday August 29th at 5:00pm. Graduate students … Continue reading →

Michal Karonski (left) who built Poland’s probabilistic combinatorics group at Poznań, and a sculpture honoring the Polish mathematicians who first broke the Enigma machine (right, with David Conlon, picture taken by Jacob Fox). Update: Here is a picture from 2015, while … Continue reading →
Paul Erdős in Jerusalem, 1933 1993 Update: Here is a link to a draft of a paper* based on the first part of this lecture. Some old and new problems in combinatorial geometry I: Around Borsuk’s problem. I just came back from … Continue reading →
Margulis’ paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis’ paper where the graphs are defined and their girth is studied. (I will come back to the question … Continue reading →
Ron Aharoni, one of Israel’s and the world’s leading combinatorialists celebrated his birthday last month. This is a wonderful opportunity to tell you about a few of the things that Ron did mainly around matching theory. Menger’s theorem for infinite … Continue reading →