Blogs about: Convexity
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Optimal Colorful Tverberg's Theorem by Blagojecic, Matschke, and Ziegler
Pavle Blagojevic, Benjamin Matschke, and Guenter Ziegler settled the “colorful Tverberg’s conjecture.” (Problem 6 in this post.) This gives a sharp version for Zivaljevic and Vreci… more →
Combinatorics and more
Convex analysis and thermodynamics
tom w wrote 3 weeks ago: A previous post briefly reviewed convex analysis. Here I’ll review the application of convexit … more →
Optimal Colorful Tverberg's Theorem by Blagojecic, Matschke, and Ziegler
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Gil Kalai wrote 1 month ago: Pavle Blagojevic, Benjamin Matschke, and Guenter Ziegler settled the “colorful Tverberg … more →
Igor Pak's "Lectures on Discrete and Polyhedral Geometry"
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Gil Kalai wrote 3 months ago: Here is a link to Igor Pak’s book on Discrete and Polyhedral Geometry (free download) . And … more →
Buffon's Needle and the Perimeter of Planar Sets of Constant Width
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Gil Kalai wrote 4 months ago: Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David E … more →
Open Problems in High Dimension Geometry
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rjlipton wrote 5 months ago: Open problems on the structure of convex bodies in high dimensions Santosh Vempala is one of world … more →
Talagrand's concentration inequality
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Terence Tao wrote 6 months ago: In the theory of discrete random matrices (e.g. matrices whose entries are random signs ), one often … more →
Test Your Intuition (5)
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Gil Kalai wrote 6 months ago: (Not such a set) consider a planar set A with the following property. In every direction, the dist … more →
Colorful Caratheodory Revisited
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Gil Kalai wrote 9 months ago: Janos Pach wrote me: ”I saw that you several times returned to the colored Caratheodory an … more →
Lovasz's Two Families Theorem
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Gil Kalai wrote 11 months ago: Laci and Kati This is the first of a few posts which are spin-offs of the extremal combinatorics ser … more →
Seven Problems Around Tverberg's Theorem
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Gil Kalai wrote 12 months ago: Imre Barany, Rade Zivaljevic, Helge Tverberg, and Sinisa Vrecica Recall the beautiful theorem of … more →
Test Your Intuition (2)
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Gil Kalai wrote 1 year ago: Question: Let be the cube in centered at the origin and having -dimensional volume equal to one. Wh … more →
Sarkaria's Proof of Tverberg's Theorem 2
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Gil Kalai wrote 1 year ago: Karanbir Sarkaria 4. Sarkaria’s proof: Tverberg’s theorem (1965): Let be points in , . … more →
Sarkaria's Proof of Tverberg's Theorem 1
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Gil Kalai wrote 1 year ago: Helge Tverberg Ladies and gentlemen, this is an excellent time to tell you about the beautiful theor … more →
Why Do So Few People Know What The English Word "More" Means?
Sonic Charmer wrote 1 year ago: A commenter chimed into this thread with the oft-emphasized, well-beloved, populist-sounding, yet ut … more →
Alright, one standard inequality
frustratum wrote 1 year ago: I’ll try to keep this blog mostly on not so standard topics. But let’s make one exceptio … more →
Helly, Cayley, Hypertrees, and Weighted Enumeration III
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Gil Kalai wrote 1 year ago: This is the third and last part of the journey from a Helly type conjecture of Katchalski and Perles … more →
Helly's Theorem, "Hypertrees", and Strange Enumeration II: The Formula
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Gil Kalai wrote 1 year ago: In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley … more →
Helly's Theorem, "Hypertrees", and Strange Enumeration I
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Gil Kalai wrote 1 year ago: 1. Helly’s theorem and Cayley’s formula Helly’s theorem asserts: For a family of n … more →
Five Open Problems Regarding Convex Polytopes
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Gil Kalai wrote 1 year ago: The problems 1. The conjecture A centrally symmetric d-polytope has at least non empty faces. 2. … more →
