Category Archives: Geometry

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 , , | 5 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 , | 9 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

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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

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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

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Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.

Lie Theory without Groups: Enumerative Geometry and Quantization of Symplectic Resolutions Our 21th Midrasha (school) IIAS, January 7 – January 12, 2018 Jerusalem Enumerative Geometry Beyond Numbers MSRI,  January 16, 2018 to May 25, 2018 Abstract for the Midrasha

Posted in Algebra and Number Theory, Combinatorics, Geometry, Updates | Leave a comment

High Dimensional Combinatorics at the IIAS – Program Starts this Week; My course on Helly-type theorems; A workshop in Sde Boker

The academic year starts today. As usual it is very hectic and it is wonderful to see the ever younger and younger students. Being a TelAvivian in residence in the last few years, I plan this year to split my … Continue reading

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Stan Wagon, TYI 32: Ladies and Gentlemen: The Answer

TYI 32, kindly offered by Stan Wagon asked A round cake has icing on the top but not the bottom. Cut out a piece in the usual shape (a sector of a circle with vertex at the center), remove it, … Continue reading

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 8 Comments

The World of Michael Burt: When Architecture, Mathematics, and Art meet.

  This remarkable 3D geometric object tiles space! It is related to a theory of “spacial networks” extensively studied by Michael Burt and a few of his students. The network associated to this object is described in the picture below. … Continue reading

Posted in Art, Combinatorics, Geometry | Tagged , , | 4 Comments