Category Archives: Analysis

Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic Factor!

Posted on October 15, 2022 by Gil Kalai

Bo’az Klartag (right) and Joseph Lehec (left) In December 2020, we reported on Yuansi Chen breakthrough result on Bourgain’s alicing problem and the Kannan Lovasz Simonovits conjecture. It is a pleasure to report on a further fantastic progress on these … Continue reading →

Posted in Analysis, Computer Science and Optimization, Convexity, Geometry, Probability | Tagged , | 3 Comments

ICM 2018 Rio (5) Assaf Naor, Geordie Williamson and Christian Lubich

Posted on January 3, 2022 by Gil Kalai

This is my fifth and last report from ICM 2018 at Rio. I will talk a little about the three Wednesday plenary talks by Assaf Naor, Geordie Williamson, and Christian Lubich. See here for other posts about ICM2018. (For the … Continue reading →

Posted in Algebra, Analysis, Geometry, ICM2018 | Tagged , , , | 3 Comments

To cheer you up in difficult times 23: the original hand-written slides of Terry Tao’s 2015 Einstein Lecture in Jerusalem

Posted on May 14, 2021 by Gil Kalai

In 2015 Terry Tao gave the Einstein lecture of the Israeli Academy for Science and Humanities. We got hold of the original signed hand-written slides of Terry’s lecture and we are happy to share them with you. The title of … Continue reading →

Posted in Analysis, Applied mathematics, Computer Science and Optimization, Physics, What is Mathematics | Tagged | 1 Comment

To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums

Posted on August 1, 2020 by Gil Kalai

Today we talk about the paper, Proof of Tomaszewski’s Conjecture on Randomly Signed Sums, by Nathan Keller and Ohad Klein. Consider a unit vector That is . Consider all () signed sums where each is either 1 or -1. Theorem … Continue reading →

Posted in Analysis, Combinatorics, Probability | Tagged , , | 12 Comments

Noam Lifshitz: A new hypercontractivity inequality — The proof!

Posted on July 24, 2020 by Gil Kalai

This is a guest post kindly contributed by Noam Lifshitz. Here is a pdf version.  This post is a continuation of the post  To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new … Continue reading →

Posted in Analysis, Combinatorics, Guest blogger | Tagged | 1 Comment

To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer

Posted on May 8, 2020 by Gil Kalai

This is a guest post kindly contributed by Noam Lifshitz. My short introduction: There is nothing like a new hypercontractivity inequality to cheer you up in difficult times and this post describes an amazing new hypercontractivity inequality.  The post describes … Continue reading →

Posted in Analysis, Combinatorics, Computer Science and Optimization, Guest blogger, Poetry, Probability | Tagged , , , , | 5 Comments

Remarkable New Stochastic Methods in ABF: Ronen Eldan and Renan Gross Found a New Proof for KKL and Settled a Conjecture by Talagrand

Posted on February 28, 2020 by Gil Kalai

  The main conjecture from Talagrand’s paper on boundaries and influences was settled by Ronen Eldan and Renan Gross. Their paper introduces a new powerful method to the field of analysis of Boolean functions (ABF). This post is devoted to … Continue reading →

Posted in Analysis, Combinatorics, Probability | Tagged , , | 7 Comments

Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson’s problem.

Posted on January 17, 2020 by Gil Kalai

A few days ago an historic 160-page paper with a very short title MIP*=RE was uploaded to the arXive by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen.  I am thankful to Dorit Aharonov and Alon Rosen … Continue reading →

Posted in Algebra, Analysis, Combinatorics, Computer Science and Optimization, Physics, Quantum | Tagged , , , , | 14 Comments

Abel in Jerusalem – SUNDAY, January 12, 2020, and other events

Posted on December 18, 2019 by Gil Kalai

Update: Boris Solomyak’s birthday conference (January 13-14, Bar-Ilan University)is now added. I would like to report on seven eight nine ten mathematical events taking place in Jerusalem, the Tel Aviv area, and Haifa in the next few weeks. (Probably I … Continue reading →

Posted in Algebra, Analysis, Combinatorics, Computer Science and Optimization, Conferences, Geometry, Updates | Tagged , , , | 1 Comment

Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe, and Marius Tiba: Flat polynomials exist!

Posted on September 9, 2019 by Gil Kalai

Béla Bollobás and Paul Erdős at the University of Cambridge in 1990. Credit George Csicsery (from the 1993 film “N is a Number”) (source) (I thank Gady Kozma for telling me about the result.) An old problem from analysis with a … Continue reading →

Posted in Analysis, Combinatorics | Tagged , , , , , | 1 Comment