Author Archives: Gil Kalai

Frankl’s Conjecture for Large Families: Ilan Karpas’ Proof

Frankl’s conjecture asserts that a for every finite family of of finite sets that is closed under union, there is an element that belongs to at least half the sets in the family. We mentioned the problem in our very … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open problems | Tagged , , , | 11 Comments

Test your intuition 33: Why is the density of any packing of unit balls decay exponentially with the dimension?

Test your intuition: What is the simplest explanation you can give to the fact that the density of every packing of unit balls in is exponentially small in ? Answers are most welcome. Of course, understanding the asymptotic behavior of … Continue reading

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 4 Comments

Serge Vlăduţ : Lattices with exponentially large kissing numbers

   (I thank Avi Wigderson for telling me about it.) Serge Vlăduţ just arxived a paper with examples of lattices in such that the kissing number is exponential in . The existence of such a lattice is a very old open … Continue reading

Posted in Combinatorics, Geometry | Tagged | 3 Comments

Peter Keevash and Eoin Long: Forbidden vector-valued intersections

Peter Keevash and Eoin Long arxived some time ago a very nice paper:  Forbidden vector-valued intersections, which settled a problem that was first posed here on the blog. Here is the abstract. We solve a generalised form of a conjecture of Kalai … Continue reading

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Peter Keevash: More and Easier Designs!

Peter Keevash just posted on the arxiv a couple of new papers on designs. The first is a rewritten version of his original paper The existence of designs with a much simpler proof. The second paper The existence of designs … Continue reading

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Monday February 19: Quantum Coding and High Dimensional Expanders

Tonight at 8:00 Israel time TCS+ Dor Misner on 2-to-2 games.    On Monday, February 19, we will have a special day on “Quantum Coding and High Dimensional Expanders” organized by Gilles Zemor. Sandwiches will be served for lunch, alongside … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Conferences, Quantum, Updates | Tagged , | 2 Comments

Alef’s Corner: There is Still a Small Gap in the Proof

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My Argument Against Quantum Computers: An Interview with Katia Moskvitch on Quanta Magazine

Quanta Magazine published an interview with me about quantum computers. It was a pleasure discussing this issue with Katia Moskvitch and I enjoyed also the photo session with David Vaaknin who also took a video of me explaining the importance of … Continue reading

Posted in Computer Science and Optimization, Physics, Quantum | Tagged , , , , | 8 Comments

The Semester Break activities of the High Dimensional Combinatorics and Expanders Special Year

UPDATE: Schedule change! An additional workshop On February 5 and shift in dats of the others. Here is the calendar We have now at HUJI a semester break, but the special semester in High dimensional combinatorics and IIAS leaded by … Continue reading

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Akshay Venkatesh Lectures at HUJI – Ostrowski’s Prize Celebration, January 24&25

Thursday January 25, 14:15-15:45 Ostrowski’s prize ceremony and Akshay Venkatesh’s prize lecture: Period maps and Diophantine problems Followed by a Basic notion lecture by Frank Calegary 16:30-17:45: The cohomology of arithmetic groups and Langlands program Wednesday January 24, 18:00-17:00: Akshay Venkatesh … Continue reading

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