Category Archives: Convexity

To cheer you up in difficult times 4: Women In Theory present — I will survive

Posted on May 11, 2020 by

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 →

Posted in Academics, Combinatorics, Computer Science and Optimization, Convexity, Games, Philosophy, Poetry, What is Mathematics, Women in science | 14 Comments

Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!

Posted on July 20, 2019 by

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 →

Posted in Combinatorics, Convexity | Tagged , | Leave a comment

Imre Bárány: Limit shape

Posted on July 9, 2019 by

Limit shapes are fascinating objects in the interface between probability and geometry and between the discrete and the continuous. This post is kindly contributed by Imre Bárány. What is a limit shape? There are finitely many convex lattice polygons contained … Continue reading →

Posted in Combinatorics, Convexity, Geometry, Guest blogger, Probability | Tagged , | 4 Comments

News on Fractional Helly, Colorful Helly, and Radon

Posted on March 15, 2019 by

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 →

Posted in Combinatorics, Convexity | Tagged , , , , , , , , , , | 3 Comments

Attila Por’s Universality Result for Tverberg Partitions

Posted on February 16, 2019 by

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 →

Posted in Combinatorics, Convexity | Tagged , , , , , , , | 7 Comments

Jean

Posted on January 2, 2019 by

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 | 5 Comments

Ricky and Branko

Posted on October 14, 2018 by

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 , | 3 Comments

Nathan Rubin Improved the Bound for Planar Weak ε-Nets and Other News From Ein-Gedi

Posted on April 5, 2018 by

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 →

Posted in Combinatorics, Convexity, Geometry, Open problems | Tagged | 4 Comments

Basic Notions Seminar is Back! Helly Type Theorems and the Cascade Conjecture

Posted on November 25, 2017 by

Kazhdan’s Basic Notion Seminar is back! The “basic notion seminar” is an initiative of David Kazhdan who joined the Hebrew University math department  around 2000. People give series of lectures about basic mathematics (or not so basic at times). Usually, speakers do … Continue reading →

Posted in Combinatorics, Convexity, Open problems | Tagged , , | 4 Comments

From Oberwolfach: The Topological Tverberg Conjecture is False

Posted on February 6, 2015 by

The topological Tverberg conjecture (discussed in this post), a holy grail of topological combinatorics, was refuted! The three-page paper “Counterexamples to the topological Tverberg conjecture” by Florian Frick gives a brilliant proof that the conjecture is false. The proof is … Continue reading →

Posted in Combinatorics, Conferences, Convexity, Updates | Tagged , , , | 3 Comments