Category Archives: Convexity

Let me tell you about three of my recent papers

  Let me tell you briefly about three of my papers that were recently accepted for publication. Relative Leray numbers via spectral sequences with Roy Meshulam, Helly-type problems with Imre Bárány, and Statistical aspects of quantum supremacy experiments with Yosi … Continue reading

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To cheer you up in difficult times 22: some mathematical news! (Part 1)

To cheer you up, in these difficult times, here are (in two parts) some mathematical news that I heard in personal communications or on social media. (Maybe I will write later, in more details,  about few of them that are … Continue reading

Posted in Combinatorics, Convex polytopes, Convexity, Geometry | Leave a comment

Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson

The Abel Prize was awarded earlier today to László Lovász and Avi Wigderson “for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.” Congratulations to Laci … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Convexity, Geometry, Updates | Tagged , , , | 3 Comments

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 | 6 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

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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

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!

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

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Imre Bárány: Limit shape

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

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

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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

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