Author Archives: Gil Kalai

Many Short Updates

Things in Berkeley and later here in Jerusalem were very hectic so I did not blog much since mid October. Much have happened so let me give brief and scattered highlights review. Two “real analysis” workshops at the Simons Institute … Continue reading

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Many triangulated three-spheres!

The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3-dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many n-vertex triangulations does the 3 … Continue reading

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NatiFest is Coming

The conference Poster as designed by Rotem Linial A conference celebrating Nati Linial’s 60th birthday will take place in Jerusalem December 16-18. Here is the conference’s web-page. To celebrate the event, I will reblog my very early 2008 post “Nati’s … Continue reading

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More around Borsuk

Piotr Achinger told me two things abour Karol Borsuk:   From Wikipedea: Dunce hat Folding. The blue hole is only for better view Borsuk trumpet is  another name for the contractible non-collapsible space commonly called also the “dunce hat“. (See … Continue reading

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Analysis of Boolean Functions – Week 7

Lecture 11 The Cap Set problem We presented Meshulam’s  bound for the maximum number of elements in a subset A of not containing a triple x,y,x of distinct elements whose sum is 0. The theorem is analogous to Roth’s theorem … Continue reading

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Analysis of Boolean Functions week 5 and 6

Lecture 7 First passage percolation 1)  Models of percolation. We talked about percolation introduced by Broadbent and Hammersley in 1957. The basic model is a model of random subgraphs of a grid in n-dimensional space. (Other graphs were considered later as … Continue reading

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Real Analysis Introductory Mini-courses at Simons Institute

The Real Analysis ‘Boot Camp’ included three excellent mini-courses. Inapproximability of Constraint Satisfaction Problems (5 lectures) Johan Håstad (KTH Royal Institute of Technology) (Lecture I, Lecture II, Lecture III, Lecture IV, Lecture V) Unlike more traditional ‘boot camps’ Johan rewarded answers and questions … Continue reading

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Analysis of Boolean Functions – week 4

Lecture 6 Last week we discussed two applications of the Fourier-Walsh plus hypercontractivity method and in this lecture we will discuss one additional application: The lecture was based on a 5-pages paper by Ehud Friedgut and Jeff Kahn: On the number … Continue reading

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Polymath 8 – a Success!

Yitang Zhang Update (July 22, ’14). The polymath8b paper “Variants of the Selberg sieve, and bounded intervals containing many primes“, is now on the arXiv. See also this post on Terry Tao’s blog. Since the last update, we also had here … Continue reading

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Analysis of Boolean Functions – Week 3

Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of Fourier-Walsh expansion of Boolean functions and the use of Hypercontractivity. Before that we  started with  a very nice discrete isoperimetric question on a … Continue reading

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