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Alex Cohen, Cosmin Pohoata, and Dmitrii Zakharov Improved the Upper Bound for...
A new upper bound for the Heilbronn triangle problem was proved by Alex Cohen, Cosmin Pohoata, and Dmitrii Zakharov. Congratulations! The paper is A new upper bound for the Heilbronn triangle problem...
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Cheerful news in difficult times: David Conlon and Jeck Lim settled Kupitz’s...
Small updates. I wrote a post about the overwhelming mathematical activities in the last week of April 2023 and the following weeks were as exciting. It was difficult to follow all the activities (not...
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What is the maximum number of Tverberg’s partitions?
The problem presented in this post was discussed in my recent lecture “New types of order types” in the workshop on discrete convexity and geometry in Budapest, a few weeks ago. The lecture described...
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Progress Around Borsuk’s Problem
I was excited to see the following 5-page paper: Convex bodies of constant width with exponential illumination number by Andrii Arman, Andrii Bondarenko, and Andriy Prymak Abstract: We show that there...
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On Viazovska’s modular form inequalities by Dan Romik
The main purpose of this post is to tell you about a recent paper by Dan Romik which gives a direct proof of two crucial inequalities in Maryna Viazovska’s proof that lattice sphere packing is the...
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Marcelo Campos, Matthew Jenssen, Marcus Michelen and, and Julian...
A few days ago, a new striking paper appeared on the arXiv A new lower bound for sphere packing by Marcelo Campos, Matthew Jenssen, Marcus Michelen, and Julian Sahasrabudhe Here is the abstract: We...
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Soma Villanyi: Every d(d+1)-connected graph is globally rigid in d dimensions.
Today, I want to tell you a little about the following paper that solves a conjecture of Laszlo Lovász and Yechiam Yemini from 1982 and an even stronger conjecture of Bob Connelly, Tibor Jordán, and...
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On the Limit of the Linear Programming Bound for Codes and Packing
Alex Samorodnitsky The most powerful general method for proving upper bounds for the size of error correcting codes and of spherical codes (and sphere packing) is the linear programming method that...
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Yair Shenfeld and Ramon van Handel Settled (for polytopes) the Equality Cases...
The power of negative thinking: Combinatorial and geometric inequalities Two weeks ago, I participated (remotely) in the discrete geometry Oberwolfach meeting, and Ramon van Handel gave a beautiful...
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Updates and Plans IV
A carpet of flowers in Shokeda, near Gaza, a few years ago. This is the fourth post of this type (I (2008); II(2011); III(2015).) I started planning this post in 2019 but as it turned out, earlier...
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Prague 2024: The First Jiří Matoušek’s Lecture
Jiří Matoušek was a great mathematician and computer scientist and a wonderful person who enlightened our communities and our lives in many ways. A few weeks ago I visited beautiful Prague (and the...
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Viterbo’s conjecture was refuted by Pazit Haim-Kislev and Yaron Ostrover
Viterbo conjecture – refuted Claude Viterbo’s 2000 volume-capacity conjecture asserts that the Euclidean (even dimensional) ball maximizes (every) symplectic capacity among convex bodies of the same...
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Celebrating Irrationality: Frank Calegari, Vesselin Dimitrov, and Yunqing...
There are very many irrational numbers but proving irrationality of a specific number is not a common event. A few weeks ago Frank Calegari, Vesselin Dimitrov, and Yunqing Tang posted a paper that...
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Some mathematical news
Update: Let me mention a ninth paper that just appeared on the arXive. IX. … and the optimal sofa for the moving sofa problem is … Gerver’s sofa. Optimality of Gerver’s Sofa, by Jineon Baek (h/t for...
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Qingyang Guan, Joseph Lehec and Bo’az Klartag Solved The Slice Conjecture!
Good news: the slice conjecture is now completely settled with combined effort of two separate papers. Qingyang Guan, A note on Bourgain’s slicing problem Abstract: This note is to study Bourgain’s...
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Test Your Intuition (57): Are All Norms Nice?
Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of . We...
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The Answer to TYI (57): In Dimension Three or More, Intuitive Norms are...
Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of . Such...
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