Category Archives: Combinatorics

TYI 41: How many steps does it take for a simple random walk on the discrete cube to reach the uniform distribution?

Aeiel Yadin’s homepage contains great lecture notes on harmonic functions on groups and on various other topics. I have a lot of things to discuss and to report; exciting developments in the analysis of Boolean functions; much to report on … Continue reading

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Gil’s Collegial Quantum Supremacy Skepticism FAQ

The first 15 samples of Google’s  53 qubit  flagship quantum supremacy experiment!   After the sensationally successful Scott’s Supreme Quantum Superiority FAQ and Boaz’s inferior classical inferiority FAQ let me add my contribution, explaining my current skeptical view. (I was actually … Continue reading

Posted in Combinatorics, Physics, Quantum | Tagged | 14 Comments

Amazing! Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park: Thresholds versus fractional expectation-thresholds

This post describes a totally unexpected breakthrough about expectation and thresholds. The result  by Frankston, Kahn, Narayanan, and Park has many startling applications and it builds on the recent breakthrough work of Alweiss, Lovett, Wu and Zhang on the sunflower … Continue reading

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Starting today: Kazhdan Sunday seminar: “Computation, quantumness, symplectic geometry, and information”

Sunday, 27 October, 2019 – 14:00 to 16:00 Repeats every week every Sunday until Sat Feb 01 2020 Location: Ross 70 See also: Seminar announcement; previous post Symplectic Geometry, Quantization, and Quantum Noise. The Google supremacy claims are discussed (with … Continue reading

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The story of Poincaré and his friend the baker

Update: After the embargo update (Oct 25): Now that I have some answers from the people involved let me make a quick update: 1) I still find the paper unconvincing, specifically, the few verifiable experiments (namely experiments that can be … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Probability, Quantum, Statistics | Tagged , , | 24 Comments

Gérard Cornuéjols’s baker’s eighteen 5000 dollars conjectures

Gérard Cornuéjols Gérard Cornuéjols‘s beautiful (and freely available) book from 2000 Optimization: Packing and Covering is about an important area of combinatorics which is lovely described in the preface to the book The integer programming models known as set packing … Continue reading

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Quantum computers: amazing progress (Google & IBM), and extraordinary but probably false supremacy claims (Google).

A 2017 cartoon from this post. After the embargo update (Oct 25): Now that I have some answers from the people involved let me make a quick update: 1) I still find the paper  unconvincing, specifically, the verifiable experiments (namely experiments … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Quantum, Updates | Tagged | 66 Comments

Jeff Kahn and Jinyoung Park: Maximal independent sets and a new isoperimetric inequality for the Hamming cube.

Three isoperimetric papers by Michel Talagrand (see the end of the post) Discrete isoperimetric relations are of great interest on their own and today I want to tell you about a new  isoperimetric inequality by Jeff Kahn and Jinyoung Park … Continue reading

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Alef’s corner: Bicycles and the Art of Planar Random Maps

The artist behind Alef’s corner has a few mathematical designs and here are two new ones. (See Alef’s  website offering over 100 T-shirt designs.)   which was used for the official T-shirt for Jean-François Le Gall’s birthday conference. See also … Continue reading

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Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe, and Marius Tiba: Flat polynomials exist!

Béla Bollobás and Paul Erdős at the University of Cambridge in 1990. Credit George Csicsery (from the 1993 film “N is a Number”) (source) (I thank Gady Kozma for telling me about the result.) An old problem from analysis with a … Continue reading

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