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- Stefan Steinerberger: The Ulam Sequence
- TYI 26: Attaining the Maximum
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- A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Three Conferences: Joel Spencer, April 29-30, Courant; Joel Hass May 20-22, Berkeley, Jean Bourgain May 21-24, IAS, Princeton
- The Quantum Computer Puzzle @ Notices of the AMS
- Stefan Steinerberger: The Ulam Sequence
- Believing that the Earth is Round When it Matters
- Seven Problems Around Tverberg's Theorem
- Helly's Theorem, "Hypertrees", and Strange Enumeration I
- Polymath10-post 4: Back to the drawing board?

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# Category Archives: Combinatorics

## Happy Birthday Richard Stanley!

This week we are celebrating in Cambridge MA , and elsewhere in the world, Richard Stanley’s birthday. For the last forty years, Richard has been one of the very few leading mathematicians in the area of combinatorics, and he found deep, profound, and … Continue reading

## Influence, Threshold, and Noise

My dear friend Itai Benjamini told me that he won’t be able to make it to my Tuesday talk on influence, threshold, and noise, and asked if I already have the slides. So it occurred to me that perhaps … Continue reading

## Levon Khachatrian’s Memorial Conference in Yerevan

Workshop announcement The National Academy of Sciences of Armenia together American University of Armenia are organizing a memorial workshop on extremal combinatorics, cryptography and coding theory dedicated to the 60th anniversary of the mathematician Levon Khachatrian. Professor Khachatrian started his … Continue reading

## Amazing: Peter Keevash Constructed General Steiner Systems and Designs

Here is one of the central and oldest problems in combinatorics: Problem: Can you find a collection S of q-subsets from an n-element set X set so that every r-subset of X is included in precisely λ sets in the collection? … Continue reading

## 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

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 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

Posted in Combinatorics, Computer Science and Optimization, Conferences, Updates
Tagged Nati Linial
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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

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 n-dimensional 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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## 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

## 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