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Category Archives: Convexity
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
Open problem session of HUJI-COMBSEM: Problem #2 Chaya Keller: The Krasnoselskii number
Marilyn Breen This is our second post on the open problem session of the HUJI combinatorics seminar. The video of the session is here. Today’s problem was presented by Chaya Keller. The Krasnoselskii number One of the best-known applications … Continue reading
Posted in Combinatorics, Convexity
Tagged Chaya Keller, Marilyn Breen, Mark Krasnoselskii, Micha A. Perles
4 Comments
To cheer you up in difficult times 4: Women In Theory present — I will survive
An amazing video (Update, May18 2020). I failed to explain what WIT is and this may have caused some misunderstanding. Here is a description from the Simons Institute site. “The Women in Theory (WIT) Workshop is intended for graduate and … Continue reading
Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!
A tweet-long summary: The cyclic polytope is wonderful and whenever we construct an analogous object we are happy. Examples: Neighborly cubic polytopes; The amplituhedron; and as of last week, the Novik-Zheng new construction of neighborly centrally symmetric spheres! At last: … Continue reading
News on Fractional Helly, Colorful Helly, and Radon
My 1983 Ph D thesis was on Helly-type theorems which is an exciting part of discrete geometry and, in the last two decades, I have had an ongoing research project with Roy Meshulam on topological Helly-type theorems. The subject found … Continue reading
Attila Por’s Universality Result for Tverberg Partitions
In this post I would like to tell you about three papers and three theorems. I am thankful to Moshe White and Imre Barany for helpful discussions. a) Universality of vector sequences and universality of Tverberg partitions, by Attila Por; Theorem … Continue reading
Jean
Jean Bourgain and Joram Lindenstrauss. I was very sad to hear that Jean Bourgain, among the greatest mathematicians of our time, and a dear friend, passed away. I first met Jean about forty years ago and later we became friends … Continue reading
Posted in Analysis, Combinatorics, Computer Science and Optimization, Convexity, Number theory, Obituary
Tagged Jean Bourgain
5 Comments
Ricky and Branko
Two dear friends, and great geometers, Ricky Pollack and Branko Grünbaum passed away a few weeks ago. Ricky was a close friend that both Mazi my wife and I loved, and we were both fascinated by his wisdom, charm and … Continue reading
Posted in Combinatorics, Convexity, Geometry, Obituary
Tagged Branko Grunbaum, Ricky Pollack
3 Comments
Nathan Rubin Improved the Bound for Planar Weak ε-Nets and Other News From Ein-Gedi
I just came back from a splendid visit to Singapore and Vietnam and I will write about it later. While I was away, Nathan Rubin organized a lovely conference on topics closed to my heart ERC Workshop: Geometric Transversals and Epsilon-Nets with … Continue reading
