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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
Posted in Combinatorics, Probability, Test your intuition
Tagged discrete cube, random walk, Test your intuition
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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
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
Posted in Combinatorics, Probability
Tagged Bhargav Narayanan, Jeff Kahn, Jinyoung Park, Keith Frankston
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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
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 Google, Henri Poincaré, quantum supremacy
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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
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 John Martinis
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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
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
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
Posted in Analysis, Combinatorics
Tagged Béla Bollobás, Flat polynomials, Julian Sahasrabudhe, Marius Tiba, Paul Balister, Robert Morris
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