# Monthly Archives: April 2018

## Testing *My* Intuition (34): Tiling High Dimension with an Arbitrary Low-Dimensional Tile.

Test your intuition 34 asked the following: A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If   can be partitioned into copies of we say that tiles . Here … Continue reading

## My Copy of Branko Grünbaum’s Convex Polytopes

Branko Grünbaum is my academic grandfather (see this highly entertaining post for a picture representing five academic generations). Gunter Ziegler just wrote a beautiful article in the Notices of the AMS on Branko Grunbaum’s  classic book “Convex Polytopes”, so this … Continue reading

Posted in Combinatorics, Convex polytopes, People | | 4 Comments

## Cohen, Haeupler, and Schulman: Explicit Binary Tree-Codes & Cancellations

The high-dimensional conference in Jerusalem is running with many exciting talks (and they are videotaped), and today in Tel Aviv there is a conference on Optimization and Discrete Geometry : Theory and Practice. Today in Jerusalem, Leonard Schulman talked (video available!) … Continue reading

## Test Your Intuition (34): Tiling high dimensional spaces with two-dimensional tiles.

A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If   can be partitioned into copies of we say that tiles . Here is a simpe example. Let consists of … Continue reading

Posted in Combinatorics, Test your intuition | Tagged | 7 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 | | 14 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 | | 13 Comments

## Conference on High Dimensional Combinatorics, April 22-26 2018

Conference on High Dimensional Combinatorics Conference home-page Dates: April 22-26, 2018 Place: Israel Institute for Advanced Studies, The Hebrew University of Jerusalem Organizers: Alex Lubotzky, Tali Kaufman and Oren Becker Registration form: click here Registration deadline: April 13, 2018 Combinatorics in general and the theory … Continue reading

## 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 | 5 Comments