- Alef Corner: Math Collaboration
- Alef’s Corner: Math Collaboration 2
- To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
- To cheer you up in difficult times 10: Noam Elkies’ Piano Improvisations and more
- Quantum Matters
- To cheer you up in difficult times 9: Alexey Pokrovskiy proved that Rota’s Basis Conjecture holds asymptotically
- To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums
- Noam Lifshitz: A new hypercontractivity inequality — The proof!
- To cheer you up in difficult times 7: Bloom and Sisask just broke the logarithm barrier for Roth’s theorem!
Top Posts & Pages
- TYI 30: Expected number of Dice throws
- Quantum Matters
- Gil's Collegial Quantum Supremacy Skepticism FAQ
- To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski's Conjecture on Randomly Signed Sums
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- A sensation in the morning news - Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture.
- Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
- Extremal Combinatorics IV: Shifting
- Are Natural Mathematical Problems Bad Problems?
Category Archives: Probability
To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums
Today we talk about the paper, Proof of Tomaszewski’s Conjecture on Randomly Signed Sums, by Nathan Keller and Ohad Klein. Consider a unit vector That is . Consider all () signed sums where each is either 1 or -1. Theorem … Continue reading
To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer
This is a guest post kindly contributed by Noam Lifshitz. My short introduction: There is nothing like a new hypercontractivity inequality to cheer you up in difficult times and this post describes an amazing new hypercontractivity inequality. The post describes … Continue reading
This post is devoted to a few memories of Boris Tsirelson who passed away at the end of January. I would like to mention that a few days ago graph theorist Robin Thomas passed away after long battle with ALS. … Continue reading
Remarkable New Stochastic Methods in ABF: Ronen Eldan and Renan Gross Found a New Proof for KKL and Settled a Conjecture by Talagrand
The main conjecture from Talagrand’s paper on boundaries and influences was settled by Ronen Eldan and Renan Gross. Their paper introduces a new powerful method to the field of analysis of Boolean functions (ABF). This post is devoted to … Continue reading
Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective
Following a lecture by Hoi Nguyen at Oberwolfach, I would like to tell you a little about the paper: Random integral matrices: universality of surjectivity and the cokernel by Hoi Nguyen and Melanie Wood. Two background questions: Hoi started with … Continue reading
In the community of mamathetitians in a certain country there are mamathetitians in two areas: Anabra (fraction p of the mamathetitians) and Algasis (fraction 1-p of mamathetitians.) There are ten universities with 50 faculty members in each mamathetics department … Continue reading
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
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
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
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