I just received an advanced copy of my very first book: “Gina Says: Adventures in the Blogsphere String War” published by Word Scientific. It is a much changed version compared to the Internet version of 8 years ago and it contains beautiful drawings by my daughter Neta Kalai. How exciting!

Here is the World Scientific page, and here is its Amazon page (paperback) and Amazon page (Kindle).

]]>

Here is another video of a smashing short talk by my dear friend Itai Benjamini with beautiful conjectures proposing an important new step in the connection between percolation and conformal geometry.

Here is the link to Itai’s original paper Percolation and coarse conformal uniformization. It turns out that the missing piece for proving the conjecture is a very interesting (innocent looking) theorem of Russo-Seymour-Welsh type.

This conjecture appears also in a paper Itai wrote with me Around two theorems and a lemma by Lucio Russo. Our paper is part of a special issue of *Mathematics and Mechanics of Complex Systems (M&MoCS), *in honor of Lucio Russo, in occasion of his retirementis. In addition to the conjectural Russo-Seymour-Welsh type theorems, we also present some developments, connections, and problems related to Russo’s lemma and Russo’s 0-1 law.

**Lucio Russo**

]]>

As we all realized waking up this morning, today is a historic day*. It is the dinner day for Alex 60^{th}‘s birthday conference, and I am thrilled to say a few words about Alex and to Alex. First let me send my love and my wife Mazi’s love to Alex and Yardena and all the family. A 60th birthday is a somber event, especially so when the birthday boy is younger than you, so I will be serious and try to move you and bring tears to your eyes, rather than try to be funny and make you laugh. (This is a new experience for me.) I will leave the many funny stories I can tell about Alex to his 70th birthday. To be on the safe side I will write them down soon so not to forget them.

I don’t know how and when Alex and I first met. Perhaps it was in 1970 or 1971 when Ron Livne (at the time a high school student like me and Alex) invited me to Tel Aviv to their “math club”. I remember meeting Alex in his home in the late 70s when we were both soldiers and he worked on his thesis and on the beautiful paper merging many different ideas and techniques using the “Golod-Shafarevich” theorem, along with Euler’s theorem for solving a well known problem. The paper appeared in the top journal of mathematics, the “Annals of Mathematics”, a rare achievement.

In 1985 I joined the Hebrew University as a faculty member, and Alex was already a professor there. When I joined the department I was in awe of the extraordinary group of people, not only in terms of their mathematical achievements, but also when their scholarly nature, their personalities, activities and interests beyond math. This feeling paralyzed me and I hoped it would pass in a couple of months. It didn’t, and even today on the verge of retirement, this is still my feeling and it extends also to the amazing group of people we hired since.

I should not tell you how extraordinarily great a mathematician Alex is, and the mathematicians here can describe Alex’s work better than I can. But to his family I want to mention a few “buzz words” reflecting some of Alex’s work: “Ramanujan graphs”, and “powerful groups,” “subgroup growth” and the “Tau property” and the “Sandwich technique” (juggling between Tao and Kazhdan’s T-poperty) , “high dimensional expanders” (I taught with Alex four times a course on this topic. At the end I may understand what it’s about) and many, many more concepts.

both to his close friends and to people who are more distant. In many cases people enjoy listening to Alex’s life-wisdom (this was already the case when he was in his twenties, even when they were much older) and advice, and confide in him their most intimate experiences and dilemmas. In these cases, the friendship relations are not quite symmetric, can we characterize what they are? It is not like the relationship you have with a father. Usually you do not want to hear words of wisdom about life from a parent and you certainly don’t want to share your intimate matters with them. It is more like the relation you have with a loving… grandfather. So you can say that Alex’s form of friendship was an early practice for grandfatherhood. Alex practiced being a grandfather all his life and now he can use his skills with his 16 and counting grandchildren. Alex is a great champion of grandchildren and I suppose he is starting to pressure his children to have grandchildren of their own about now.

This is why he and Yardena settled in Efrat, this is why he worked hard to save and advance the “Israel Journal of Mathematics”, and this is why he went into politics. Alex joined politics in 95 and the Israeli parliament after the 99 elections. (A major upset at the time. Commentators and polls predicted victory for one candidate but the other candidate won. This happens from time to time*.) I remember talking with Hillel about hosting a farewell party for Alex. Hillel was surprised that a mathematical genius like Alex would join the parliament and I thought he would never come back.

Alex had a lot of virtues and two weaknesses as a leader and a politician. Alex was very smart and he could understand the fine details as well as the large picture. He befriended and connected well with other politicians from all parties. In politics and administration just like in mathematics, he could identify the important problems and he went head on to tackle them. He is famous for the Beilin-Lubotzky convention for relations between orthodox and non-orthodox Jews and many other related issues. One of his weaknesses is that he is not malicious and does not appreciate the joy of malice. As in mathematics, also in politics and in academic administration, he could identify the important problems and he went head on to tackle them. He was also the founder of the committee for the status of women in the Israeli parliament. [Here, in the lecture, Alex corrected me and said that I am exaggerating and he was not the founder. But I made the mistake on purpose to make another point.] … Right, Alex was an active member of this committee, not the founder. It was founded 4 years earlier by Yael Dayan (Moshe Dayan’s daughter). This brings me to the second weakness of Alex as a politician. He is too honest. Most politicians and also a few mathematicians will not correct an undeserved credit.

Alex comes from a family of holocaust survivors and to a large extent regards himself as one. In my impression this accounts primarily for his immense gratitude for what he was blessed with, including the sweet life of a mathematician. It is also related to a principle he has of never wasting food and never wasting time. We shared apartments quite a few times and he also refused to throw away food. (About Alex’s cooking wait 10 years.) Once I visited him and Yardena when they were renting a house filled with spoiled non kosher food that had been left by the owner and I secretly threw away most of it. A legacy from Alex’s father Issar is never to waste time. (I mean time when one is awake, this does not include sleeping, we already heard stories about Alex’s sacred afternoon sleep.) “A time being wasted is like a time being dead,” Alex once told me when he caught me playing a computer game at the computer room at Yale. (I wonder how this statement could be scientifically verified.) Since then I was careful to quickly move to a different screen when Alex entered the computer room.

You can read about the remarkable history of Alex’s parents in WW2 in Asael’s soon to be published second book.

And I want to conclude with mentioning Alex as a father to Asael, and how Alex and Yardena handles Asael’s grave injury in 2006. I remember Mazi and I had dinner with Alex and Yardena and Avi and Edna a day or two before Alex and Yardena got the news that Asael was injured and that was in critical condition. This was a terrible ordeal and a difficult struggle, mainly for Asael but also for his parents and the entire family. Asael, now a medical doctor as well as a researcher, wrote his first book about his experiences, and has recently been translated to English.

Let me send again love from Mazi, myself and my children to Alex, Yardena and the family and wish Alex many more years. I haven’t talked about many joint adventures from the Jordan river to the Amazonas. I promise to be funny ten years from now.

**At that day November 9, 2016, we woke up in the morning realizing that Donald Trump was the newly-elected President of the United States. Efim Zelmanov mentioned in his after dinner speech that Alex did not share the universal confidence that Trump will not be elected.*

]]>

(see also pdf version) ? Quantum computing is one of the most exciting developments of computer science in the last decades. But this concept is not without its critics, often known as “quantum computing…]]>

Boaz Barak wrote a nice essay which I reblog to you below about skepticism of quantum computers. His essay is centered around a description of four scenarios (or possible “worlds” in the style of Russel Impagliazzo) about the matter. Boaz’ world are called

Superiorita(quantum computers are realistic and computational superior),Popscitopia(Quantum computers are realistic and can solve NP-complete problems), Skepticland(quantum computers are not realistic),and Classicatopia(quantum algorithms can efficiently be simulated on a classical computers).Apropos Russel’s universes, Boaz told me about a new cryptography “world” called Obfustopia that can be found (along with some modification of the original worlds) in Boaz’ survey paper. I heard about it and about the related important LWE (learning with errors) problem also from Alon Rosen.

Boaz’ essay also includes Boaz’ own optimistic personal view and also some very brief critique of my skeptical stance. Boaz conclude his personal opinion with:

The bottom line is that, as far as I can tell, Superiorita is the most beautiful and evidence-supported world that is currently on offer.Boaz’ main argument for his point of view is:

…as far as I can tell, these engineering difficulties are not fundamental barriers and with sufficient hard work and resources the noise can be driven down to as close to zero as needed.This is indeed the crux of matters and my analysis gives good reasons to think that Boaz is not correct. The different opinions are described in the pictures below and the crux of matters is “can we cross the

green line?”

Common expectationsIt is a common belief that by putting more effort for creating

qubitsthe noise level can be pushed down to as close to zero as we want. Once the noise level is small enough and cross thegreen line,quantum error correction allowslogical qubitsreducing the noise even further with small amount of additional effort . Very high qualitytopological qubitsare also expected.

The picture suggested by my analysisMy analysis (see here and here and here) gives good reasons to expect that we will not be able to reach the

green lineand that all attempts forlogicalandtopologicalqubits will yield bad quality qubits.## Finer Worlds

One can make a finer division of the superiorita world, and, in my view, the three most relevant worlds are the following:

Quantopia– The model of quantum circuits is the correct description of local quantum systems in nature and therefore universal quantum computation is possible. Quantum supremacy and robust quantum information are present and perhaps even ubiquitous in the physical world. Quantum systems, quantum information and computation are analogous to classical systems, classical information and computation. Quantum error correction is analogous to classical error correction: an important engineering tool but not the thing that makes the qualitative difference whether scalabale communication or computation is possible. (This represents Boaz’ beliefs expressed in his post and his later comments.)

Superiorita(Quantum noise below the threshold.) Quantum systems are inherently noisy. Time-dependent quantum evolutions necessarily interacts with the environment and are therefore noisy. The model of noisy quantum circuits is the correct description of local quantum systems in nature. Quantum error-correction shows that small islands representing noiseless quantum circuits can be created and may also exist in nature. Hence quantum computation is possible. (This is perhaps the most common view among researchers in quantum information.)

Skeptica– (Quantum noise above the threshold.) Quantum systems are inherently noisy. Time-dependent quantum evolutions necessarily interacts with the environment. The model of noisy quantum circuits is the correct description of local quantum systems in nature. The noise level cannot be pushed below the level allowing quantum error-correction and quantum fault-tolerance. Hence quantum computation is not possible. Quantum supremacy is not demonstrated in nature and cannot be demonstrated in the laboratory. (This is were I stand).There are, of course people who are skeptical about quantum computers from other reasons like the young Boaz who simply did not like physics. There are people who for various reasons are skeptical of quantum mechanics.

Quantopia suggests that “quantum supremacy” and “robust quantum information” will be present and in fact ubiquitous in the physical world, while under ” superiorita” quantum supremacy represents rare a islands inside a large “decoherence desert” (as Daniel Gottesman referred to it in his beautiful picture portrayed in this post.) The difference between quantopia and superiorita is relevant to Scott Aaronson’s hope that quantum computers promise

trillion dollarsindustry via simulations. While additional computing power is always welcome this idea is less promising in the superiorita scenario where the usefulness of quantum computers to simulation is less clear.Anyway, here is Boaz’ piece.

(see also pdf version)

*Quantum computing* is one of the most exciting developments of computer science in the last decades. But this concept is not without its critics, often known as “quantum computing skeptics” or “skeptics” for short. The debate on quantum computing can sometimes confuse the *physical* and *mathematical* aspects of this question, and so in this essay I try to clarify those. Following Impagliazzo’s classic essay, I will give names to scenarios or “potential worlds” in which certain physical or mathematical conditions apply.

**Superiorita** is the world where it is feasible to build scalable quantum computers, and these computers have exponential advantage over classical computers. That is, in superiorita there is no fundamental physical roadblock to building large quantum computers, and hence the class BQP is a good model of computation that is physically realizable. More precisely, in superioriata the amount of resources (think…

View original post 2,547 more words

]]>

]]>

Answer at your free will

]]>

Avi Wigderson is one of the most prolific and creative theoretical computer scientists (in fact, he is one of the most prolific and creative scientists, period). Over the last several years, Avi had worked…]]>

The joyous lion of theoretical computer science(Read here a story about Avi and me related to the above picture.)

Boaz Barak is reporting on Avi Wigderson’s book Mathematics and Computation which is on Avi’s homepage. I read through an earlier version and it is highly recommended! Let me also recommend Avi’s earlier survey on interaction between CS and math.

Avi Wigderson is one of the most prolific and creative theoretical computer scientists (in fact, he is one of the most prolific and creative scientists, period). Over the last several years, Avi had worked hard into distilling his vast knowledge of theoretical computer science and neighboring fields into a book surveying TCS, and in particular computational complexity, and its connections with mathematics and other areas.

I’m happy to announce that he’s just put a draft of this upcoming book on his webpage.

The book contains a high level overview of TCS, starting with the basics of complexity theory, and moving to areas such as circuit complexity, proof complexity, distributed computing, online algorithms, learning, and many more. Along the way there are interludes about the connections of TCS to many mathematical areas.

The book is highly recommended for anyone, but in particular for undergraduate and beginning graduate students that are interested…

View original post 140 more words

]]>

Let me tell you about a special year taking place at the Israeli Institute of Advanced Science at Jerusalem on Geometric, Topological and Computational Aspects of High-Dimensional Combinatorics, the opening workshop of this conference at Sde boker, and my course on Helly-type theorems.

organized by Alexander Lubotzky and Tali Kaufman

The web page of the semester is here. And the summary of its activity is:

Combinatorics in general and the theory of expander graphs, in particular, have been fruitful areas of interaction of pure and applied mathematics. In recent years a “high dimensional” theory has emerged. This theory, aside from its intellectual interest, also has great potential for various applications in mathematics and computer science. This theory calls for a collaboration of experts in combinatorics, topology, geometry, group theory and computer science. We propose to organize a program that will bring together people from these areas in order to create a community of scholars who can collaborate on these new challenges.

Starting tomorrow there will be a full day of activities every Monday with some additional activities on Sunday and Thursday.

9:00 – 11:00 – “High Dimensional Expanders and Group Stability”, a course by Alex Lubotzky

——————————–

11:00 – 12:30 – Combinatorics research seminar

(this is the usual combinatorics seminar, which takes place in the IIAS this year instead of in the computer science building)

Organizer: Karim Adiprasito (karim.adiprasito@mail.huji.ac.il)

Upcoming talk (Oct. 23): “Counting lattice points inside a d-dimensional polytope via Fourier analysis”, Quang Nhat Le

——————————–

14:00 – 16:00 – “Afternoon learning seminar on high dimensional combinatorics”, talks and series of talks by various lecturers, intended for studying various topics together

Upcoming talk (Oct. 23): “High-dimensional permutations”, Nati Linial

On Thursdays at 11 I will give a course on Helly-type theorems which is with some relations to the special year. (Time may change.)

Next week there will be an opening workshop at Sde Boker

Great topics!

]]>

A round cake has icing on the top but not the bottom. Cut out a piece in the usual shape

(a sector of a circle with vertex at the center), remove it, turn it upside down, and replace

it in the cake to restore roundness. Do the same with the next piece; If the central angle

of the pieces is 181°, what is the number of steps needed so that, under repeated cutting-and flipping, all icing returns to the top of the cake?

Here are your answers:

And the correct answer is:

]]>

A round cake has icing on the top but not the bottom. Cut out a piece in the usual shape

(a sector of a circle with vertex at the center), remove it, turn it upside down, and replace

it in the cake to restore roundness. Do the same with the next piece; i.e., take a piece

with the same vertex angle, but rotated counterclockwise from the first one so that one

boundary edge coincides with a boundary edge of the first piece. Remove it, turn it

upside-down, and replace it. Keep doing this in a counterclockwise direction. The figure

shows the situation after two steps when the central angle is 90°. If θ is the central angle

of the pieces, let f (θ) be the number of steps needed so that, under repeated cutting-andflipping just described, all icing returns to the top of the cake, with f (θ) set to ∞ if this

never happens. For example, f(90°) = 8.

Source info:

The original source of this problem was Problem 31.2.8.3 in the 1968 Moscow Math Olympiad [L, p. 90] in a slightly different form. The variant given here is in [Winkler].

[L] 60-odd years of Moscow Mathematical Olympiads, G. Leites editor, G. Halperin, A Tolpygo, P Grozman A Shapovalov, V Prasolov, A Fomenko

[W] Mathematical Mind-Benders by Peter Winkler, published by AK Peters, Wellesley, Mass., 2007.

(see here)

]]>