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Category Archives: Geometry
Micha Perles’ Geometric Proof of the Erdos-Sos Conjecture for Caterpillars
A geometric graph is a set of points in the plane (vertices) and a set of line segments between certain pairs of points (edges). A geometric graph is simple if the intersection of two edges is empty or a vertex … Continue reading
Touching Simplices and Polytopes: Perles’ argument
Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection) The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Joseph Zaks, Micha A. Perles
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Jozsef Solymosi is Giving the 2017 Erdős Lectures in Discrete Mathematics and Theoretical Computer Science
May 4 2:30-3:30; May 7 11:00-13:00; May 10 10:30-12:00 See the event webpage for titles and abstracts (or click on the picture below).
Around the Garsia-Stanley’s Partitioning Conjecture
Art Duval, Bennet Goeckner, Carly Klivans, and Jeremy Martin found a counter example to the Garsia-Stanley partitioning conjecture for Cohen-Macaulay complexes. (We mentioned the conjecture here.) Congratulations Art, Bennet, Carly and Jeremy! Art, Carly, and Jeremy also wrote an article on the … Continue reading
Posted in Combinatorics, Geometry
Tagged Art Duval, Bennet Goeckner, Carly Klivans, Garsia-Stanley conjecture, Jeremy Martin, Ping Zhang
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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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