Category Archives: Geometry

Beyond the g-conjecture – algebraic combinatorics of cellular spaces I

The g-conjecture for spheres is surely the one single conjecture I worked on more than on any other, and also here on the blog we had a sequence of posts about it by Eran Nevo (I,II,III,IV). Here is a great … Continue reading

Posted in Combinatorics, Convex polytopes, Geometry | Tagged , , , , , , , , , , , , , , , | 6 Comments

An Interview with Yisrael (Robert) Aumann

I was privileged to join Menachem Yaari and Sergiu Hart in interviewing Yisrael Aumann.  The interview is in Hebrew. It is an initiative of the Israel Academy of Sciences and the Humanities. For our non Hebrew speakers here is in … Continue reading

Posted in Academics, Combinatorics, Games, Geometry, Rationality | Tagged , , | 1 Comment

Igor Pak is Giving the 2018 Erdős Lectures in Discrete Mathematics and Theoretical Computer Science

Update: The lectures this week are cancelled.  They will be given at a later date. Next week Igor Pak will give the 2018 Erdős Lectures   Monday Jun 18 2018 Combinatorics — Erdos lecture: Igor Pak (UCLA) “Counting linear extensions” 11:00am to 12:30pm Location: … Continue reading

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Sailing into High Dimensions

On June 20 at 13:30 I talk here at HUJI about Sailing into high dimensions. (Thanks to Smadar Bergman for the poster.)

Posted in Combinatorics, Geometry, Updates | Tagged | 2 Comments

Coloring Problems for Arrangements of Circles (and Pseudocircles)

To supplement and celebrate Aubrey de Grey’s result here are Eight problems on coloring circles A) Consider a finite family of unit circles. What is the minimum number of colors needed to color the circles so that tangent circles are … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged , , | 8 Comments

Aubrey de Grey: The chromatic number of the plane is at least 5

  A major progress on an old standing beautiful problem. Aubrey de Grey proved that the chromatic number of the plane is at least 5. (I first heard about it from Alon Amit.) The Hadwiger–Nelson problem asks for the minimum number of … Continue reading

Posted in Combinatorics, Geometry, Open problems, Updates | Tagged , | 10 Comments

Nathan Rubin Improved the Bound for Planar Weak ε-Nets and Other News From Ein-Gedi

I just came back from a splendid visit to Singapore and Vietnam and I will write about it later. While I was away, Nathan Rubin organized a lovely conference on topics closed to my heart  ERC Workshop: Geometric Transversals and Epsilon-Nets with … Continue reading

Posted in Combinatorics, Convexity, Geometry, Open problems | Tagged | 1 Comment

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 | 4 Comments

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

Posted in Algebra and Number Theory, Computer Science and Optimization, Geometry, Updates | Tagged , , | Leave a comment