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Category Archives: Geometry
Jirka
The Mathematics of Jiří Matoušek is a conference taking place this week at Prague in memory of Jirka Matoušek. Here are the slides of my planned talk on Maestro Jirka Matoušek. This post presents the opening slides for the conference … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Conferences, Geometry, Obituary
Tagged Jirka Matoušek
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The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.
Here is the abstract of a recent paper by Andrew Suk. (I heard about it from a Facebook post by Yufei Zhao. I added a link to the original Erdős Szekeres’s paper.) Let ES(n) be the smallest integer such that … Continue reading
Three Conferences: Joel Spencer, April 29-30, Courant; Joel Hass May 20-22, Berkeley, Jean Bourgain May 21-24, IAS, Princeton
Dear all, I would like to advertise three promising-to-be wonderful mathematical conferences in the very near future. Quick TYI. See if you can guess the title and speaker for a lecture described by “where the mathematics of Cauchy, Fourier, Sobolev, … Continue reading
Posted in Analysis, Combinatorics, Conferences, Geometry, Updates
Tagged Jean Bourgain, Joel Hass, Joel Spencer
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A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
Maryna Viazovska The news Maryna Viazovska has solved the densest packing problem in dimension eight! Subsequently, Maryna Viazovska with Henry Cohn, Steve Miller, Abhinav Kumar, and Danilo Radchenko solved the densest packing problem in 24 dimensions! Here are the links to … Continue reading
Many triangulated three-spheres!
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 Eran Nevo, Stedman Wilson
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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
Some old and new problems in combinatorics and geometry
Paul Erdős in Jerusalem, 1933 1993 Update: Here is a link to a draft of a paper* based on the first part of this lecture. Some old and new problems in combinatorial geometry I: Around Borsuk’s problem. I just came back from … Continue reading
Andriy Bondarenko Showed that Borsuk’s Conjecture is False for Dimensions Greater Than 65!
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
