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# Category Archives: Computer Science and Optimization

## 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

## Analysis of Boolean functions – week 2

Post on week 1; home page of the course analysis of Boolean functions Lecture II: We discussed two important examples that were introduced by Ben-Or and Linial: Recursive majority and tribes. Recursive majority (RM): is a Boolean function with variables … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Boolean functions, Tribes
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## 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

## BosonSampling and (BKS) Noise Sensitivity

Update (Nov 2014): Noise sensitivity of BosonSampling and computational complexity of noisy BosonSampling are studied in this paper by Guy Kindler and me. Some of my predictions from this post turned out to be false. In particular the noisy BosonSampling … Continue reading

Posted in Computer Science and Optimization, Physics, Probability
Tagged BosonSampling, Noise, Noise-sensitivity, Quantum computation
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## Lawler-Kozdron-Richards-Stroock’s combined Proof for the Matrix-Tree theorem and Wilson’s Theorem

David Wilson and a cover of Shlomo’s recent book “Curvature in mathematics and physics” A few weeks ago, in David Kazhdan’s basic notion seminar, Shlomo Sternberg gave a lovely presentation Kirchhoff and Wilson via Kozdron and Stroock. The lecture is based on … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability
Tagged David Wilson, Gustav Kirchhoff, Trees
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## The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava

…while we keep discussing why mathematics is possible… The news Adam Marcus, Dan Spielman, and Nikhil Srivastava posted a paper entitled “Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem,” where they prove the 1959 Kadison-Singer conjecture. (We discussed part … Continue reading

## Why is mathematics possible?

Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory. As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading

## QSTART

Physics, Computer Science, Mathematics, and Foundations’ views on quantum information Inauguration conference for the Quantum Information Science Center (QISC), Hebrew university of Jerusalem Update: The news of our conference have made it to a big-league blog. Update (July 2013): QStart … Continue reading

## My Quantum Debate with Aram III

This is the third and last post giving a timeline and some non technical highlights from my debate with Aram Harrow. Where were we After Aram Harrow and I got in touch in June 2011, and decided to have … Continue reading