Search Results for: erdos

The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond

A quick schematic road-map to these new geometric objects. The  positroidron can be seen as a cellular structure on the nonnegative Grassmanian – the part of the real Grassmanian G(m,n) which corresponds to m by n matrices with all m by … Continue reading

Posted in Algebra and Number Theory, Combinatorics, Convex polytopes, Physics | Tagged , , , , , , | 1 Comment

When Do a Few Colors Suffice?

When can we properly color the vertices of a graph with a few colors? This is a notoriously difficult problem. Things get a little better if we consider simultaneously a graph together with all its induced subgraphs. Recall that an … Continue reading

Posted in Combinatorics | Tagged | 1 Comment

School Starts at HUJI

We are now starting the third week of the academic year at HUJI. As usual, things are very hectic, a lot of activities in the mathematics department, in our sister CS department, around in the campus, and in our combinatorics … Continue reading

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Happy Birthday Ervin, János, Péter, and Zoli!

The four princes in summit 200, ten years ago. (Left to right) Ervin Győri, Zoltán Füredi, Péter Frankl and János Pach   In 2014, Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach are turning 60 and summit 240 is a conference … Continue reading

Posted in Conferences, Happy birthday | 3 Comments

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

Posted in Combinatorics, Conferences, Happy birthday | Tagged | 3 Comments

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

Posted in Combinatorics, Conferences | Tagged | 1 Comment

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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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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Around Borsuk’s Conjecture 3: How to Save Borsuk’s conjecture

Borsuk asked in 1933 if every bounded set K of diameter 1 in can be covered by d+1 sets of smaller diameter. A positive answer was referred to as the “Borsuk Conjecture,” and it was disproved by Jeff Kahn and me in 1993. … Continue reading

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Analysis of Boolean Functions – week 1

Home page of the course. In the first lecture I defined the discrete n-dimensional cube and  Boolean functions. Then I moved to discuss five problems in extremal combinatorics dealing with intersecting families of sets. 1) The largest possible intersecting family … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Teaching | Tagged , , , | 1 Comment