Levon Khachatrian’s Memorial Conference in Yerevan

Workshop announcement The National Academy of Sciences of Armenia together American University of Armenia are organizing a memorial workshop on extremal combinatorics, cryptography and coding theory dedicated to the 60th anniversary of the mathematician Levon Khachatrian.  Professor Khachatrian started his … Continue reading

Analysis of Boolean Functions week 5 and 6

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 n-dimensional space. (Other graphs were considered later as … Continue reading

Analysis of Boolean Functions – Week 3

Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we  started with  a very nice discrete isoperimetric question on a … Continue reading

Around Borsuk’s Conjecture 3: How to Save Borsuk’s conjecture

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

Analysis of Boolean Functions – week 1

Home page of the course. In the first lecture I defined the discrete n-dimensional 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

Open Collaborative Mathematics over the Internet – Three Examples

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 47-minutes … Continue reading

Analysis of Boolean Functions

This fall I am giving a course at Berkeley on analysis of Boolean functions Course number: CS 294-92 Title: Analysis of Boolean Functions Lectures: TuTh 5:00-6:30 Location: Room 310 Soda First lecture will be was on Thursday August 29th at 5:00pm. Graduate students … Continue reading