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 Mathematical Gymnastics
 Media Item from “Haaretz” Today: “For the first time ever…”
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
 Media items on David, Amnon, and Nathan
 Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes
 Happy Birthday Ervin, János, Péter, and Zoli!
 My Mathematical Dialogue with Jürgen Eckhoff
 Test Your Intuition (23): How Many Women?
 Happy Birthday Richard Stanley!
Top Posts & Pages
 Believing that the Earth is Round When it Matters
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 The Ultimate Riddle
 Why Quantum Computers Cannot Work: The Movie!
 Two Math Riddles
 Analysis of Boolean Functions
 The Intermediate Value Theorem Applied to Football
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota's Conjecture on Matroids
 Polymath 8  a Success!
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Author Archives: Gil Kalai
Many triangulated threespheres!
The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many nvertex triangulations does the 3 … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Eran Nevo, Stedman Wilson
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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 1618. Here is the conference’s webpage. To celebrate the event, I will reblog my very early 2008 post “Nati’s … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Conferences, Updates
Tagged Nati Linial
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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 noncollapsible space commonly called also the “dunce hat“. (See … Continue reading
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
Posted in Combinatorics, Computer Science and Optimization, Teaching
Tagged Cap set problem, Codes, Linearity testing
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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 ndimensional space. (Other graphs were considered later as … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability, Teaching
Tagged Arrow's theorem, Percolation
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Real Analysis Introductory Minicourses at Simons Institute
The Real Analysis ‘Boot Camp’ included three excellent minicourses. 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
Analysis of Boolean Functions – week 4
Lecture 6 Last week we discussed two applications of the FourierWalsh plus hypercontractivity method and in this lecture we will discuss one additional application: The lecture was based on a 5pages paper by Ehud Friedgut and Jeff Kahn: On the number … Continue reading
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
Analysis of Boolean Functions – Week 3
Lecture 4 In the third week we moved directly to the course’s “punchline” – the use of FourierWalsh expansion of Boolean functions and the use of Hypercontractivity. Before that we started with a very nice discrete isoperimetric question on a … Continue reading
Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found
The upper bound theorem asserts that among all ddimensional polytopes with n vertices, the cyclic polytope maximizes the number of facets (and kfaces for every k). It was proved by McMullen for polytopes in 1970, and by Stanley for general triangulations … Continue reading