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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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