Category Archives: Geometry

Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes

Posted on July 16, 2014 by

Special Quantum PCP and/or Quantum Codes: Simplicial Complexes and Locally Testable CodesDay בי”ס להנדסה ולמדעי המחשב 24 Jul 2014 – 09:30 to 17:00 room B-220, 2nd floor, Rothberg B Building On Thursday, the 24th of July we will host a SC-LTC (simplicial complexes … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Conferences, Geometry, Quantum | Tagged , , , , , , , , , | Leave a comment

Many triangulated three-spheres!

Posted on November 28, 2013 by

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 , | Leave a comment

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

Posted on September 4, 2013 by

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 →

Posted in Combinatorics, Convexity, Geometry, Open problems | Tagged , , , | Leave a comment

Some old and new problems in combinatorics and geometry

Posted on July 6, 2013 by

Paul Erdős in Jerusalem, 1933  1993 I just came back from a great Erdős Centennial conference in wonderful Budapest. I gave a lecture on old and new problems (mainly) in combinatorics and geometry (here are the slides), where I presented twenty … Continue reading →

Posted in Combinatorics, Geometry, Open problems | Tagged | 4 Comments

Andriy Bondarenko Showed that Borsuk’s Conjecture is False for Dimensions Greater Than 65!

Posted on May 27, 2013 by

The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for two-distance sets  that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading →

Posted in Combinatorics, Geometry, Open problems | Tagged , , , , | 2 Comments

F ≤ 4E

Posted on February 1, 2013 by

1. E ≤ 3V Let G be a simple planar graph with V vertices and E edges. It follows from Euler’s theorem that E ≤ 3V In fact, we have (when V is at least 3,) that E ≤ 3V – 6. … Continue reading →

Posted in Combinatorics, Convex polytopes, Geometry, Open problems | Tagged | 12 Comments

Symplectic Geometry, Quantization, and Quantum Noise

Posted on January 1, 2013 by

Over the last two meetings of our HU quantum computation seminar we heard two talks about symplectic geometry and its relations to quantum mechanics and quantum noise. Yael Karshon: Manifolds, symplectic manifolds, Newtonian mechanics, quantization, and the non squeezing theorem. … Continue reading →

Posted in Computer Science and Optimization, Geometry, Physics | Tagged , , , , , , | 6 Comments

Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)

Posted on April 10, 2012 by

Wolfgang Haken found an algorithm to tell if a knot is trivial, and, more generally with Hemion, if two knots are equivalent. Joel Hass, Jeff Lagarias and Nick Pippinger proved in 1999 that telling that a knot is unknotted is … Continue reading →

Posted in Computer Science and Optimization, Geometry | Tagged | 8 Comments

Exciting News on Three Dimensional Manifolds

Posted on April 1, 2012 by

The Virtually Haken Conjecture A Haken 3-manifold is a compact 3-dimensional manifold M which is irreducible (in a certain strong sense) but contains an incompressible surface S. (An embedded surface S is incompressible if the embedding indices an injection of its … Continue reading →

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

Fractional Sylvester-Gallai

Posted on January 20, 2012 by

Avi Wigderson was in town and gave a beautiful talk about an extension of Sylvester-Gallai theorem. Here is a link to the paper: Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes by Boaz Barak, Zeev … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry | Tagged , , , | 4 Comments