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Category Archives: Geometry
Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.
Stavros Argyrios Papadakis, Vasiliki Petrotou, and Karim Adiprasito In 2018, I reported here about Karim Adiprasito’s proof of the g-conjecture for simplicial spheres. This conjecture by McMullen from 1970 was considered a holy grail of algebraic combinatorics and it resisted … Continue reading
Posted in Algebra, Combinatorics, Geometry
Tagged g-conjecture, Hilda Geiringer, Karim Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
4 Comments
Igor Pak: What if they are all wrong?
Originally posted on Igor Pak's blog:
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some…
Posted in Combinatorics, Computer Science and Optimization, Geometry, What is Mathematics
Tagged Igor Pak
6 Comments
Open problem session of HUJI-COMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem
This post continues to describe problems presented at our open problems session back in November 2020. Here is the first post in the series. Today’s problem was presented by me, and it was an old 1989 conjecture of mine. A … Continue reading
To Cheer You Up in Difficult Times 15: Yuansi Chen Achieved a Major Breakthrough on Bourgain’s Slicing Problem and the Kannan, Lovász and Simonovits Conjecture
This post gives some background to a recent amazing breakthrough paper: An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture by Yuansi Chen. Congratulations Yuansi! The news Yuansi Chen gave an almost constant bounds for Bourgain’s … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Convexity, Geometry
Tagged Yuansi Chen
4 Comments
Recent progress on high dimensional Turan-Type problems by Andrey Kupavskii, Alexandr Polyanskii, István Tomon, and Dmitriy Zakharov and by Jason Long, Bhargav Narayanan, and Corrine Yap.
The extremal number for surfaces Andrey Kupavskii, Alexandr Polyanskii, István Tomon, Dmitriy Zakharov: The extremal number of surfaces Abstract: In 1973, Brown, Erdős and Sós proved that if is a 3-uniform hypergraph on vertices which contains no triangulation of the sphere, then … Continue reading
Open problem session of HUJI-COMBSEM: Problem #1, Nati Linial – Turan type theorems for simplicial complexes.
On November, 2020 we had a very nice open problem session in our weekly combinatorics seminar at HUJI. So I thought to have a series of posts to describe you the problems presented there. This is the first post in … Continue reading
Péter Pál Pach and Richárd Palincza: a Glimpse Beyond the Horizon
Prologue Consider the following problems: P3: What is the maximum density of a set A in without a 3-term AP? (AP=arithmetic progression.) This is the celebrated Cap Set problem and we reported here in 2016 the breakthrough results by … Continue reading
Posted in Combinatorics, Geometry, Number theory, Open problems
Tagged Péter Pál Pach, Richárd Palincza
9 Comments
To cheer you up in difficult times 13: Triangulating real projective spaces with subexponentially many vertices
Wolfgang Kühnel Today I want to talk about a new result in a newly arXived paper: A subexponential size by Karim Adiprasito, Sergey Avvakumov, and Roman Karasev. Sergey Avvakumov gave about it a great zoom seminar talk about the result … Continue reading
Posted in Algebra, Combinatorics, Geometry
Tagged Karim Adiprasito, Roman Karasev, Sergey Avvakumov, Wolfgang Kuhnel
1 Comment
Alef’s Corner: Math Collaboration 2
Other Alef’s corner posts
