From top left clockwise: Alexander Gaifullin, Denis Gorodkov, Ulrich Brehm, Wolfgang Kühnel

Here is the paper:

Alexander A. Gaifullin: 634 vertex-transitive and more than 10¹⁰³ non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective plane

**Abstract with annotation:**

In 1987 Brehm and Kühnel showed that any combinatorial -manifold with less than vertices is PL homeomorphic to the sphere and any combinatorial -manifold with exactly vertices is PL homeomorphic to either the sphere or a manifold like a projective plane in the sense of Eells and Kuiper. The latter possibility may occur for only.

This is a lovely theorem and the proof is based on Morse theoretic ideas, The study was motivated by the theory of tight embeddings of manifolds in differential geometry.

There exist a unique 6-vertex triangulation of ,

This is a wonderful object obtained by identifying opposite faces of an icosahedron.

a unique 9-vertex triangulation of ,

This is an amazing mathematical construction by Kühnel and Lassman from 1983.

and at least three 15-vertex triangulations of . (We mentioned it in this post.)

Those were constructed in 1992 by Brehm and Kühnel. Gorodkov proved in 2019 that the Brehm–Kühnel complexes are indeed PL homeomorphic to .

However, until now, the question of whether there exists a 27-vertex triangulation of a manifold like the octonionic projective plane has remained open. We solve this problem by constructing a lot of examples of such triangulations. Namely, we construct 634 vertex-transitive 27-vertex combinatorial 16-manifolds like the octonionic projective plane. Four of them have symmetry group of order 351, and the other 630 have symmetry group of order 27. Further, we construct more than non-vertex-transitive 27-vertex combinatorial 16-manifolds like the octonionic projective plane. Most of them have trivial symmetry group, but there are also symmetry groups , , and . We conjecture that all the triangulations constructed are PL homeomorphic to the octonionic projective plane . Nevertheless, we have no proof of this fact so far.

(Actually one can even expect that in the Brehm-Kühnel theorems all triangulations of manifolds with vertices are PL projective planes over the Reals, Quaternions or Octanions.)

I heard about the new result from Wolfgang Kühnel who wrote me: “I’m quite surprised that an object with such a huge *f*-vector can be constructed at all.”

The seek for a triangulation of a manifold like a projective plane with vertices (now completed by Gaifullin) reminded me of the situation of Moore graphs of girth five. A Moore graph is a regular -graph with diameter , and girth . (It must have vertices.)

The **Hoffman–Singleton theorem** states that any Moore graph with girth 5 must have degree 2, 3, 7, or 57. There are known examples for degrees 2, 3 and 7, and the existence of a Moore graph of girth 5 and degree 57 is one of the great mysteries of mathematics.

We can ask, more generally, about -neighborly triangulations of manifolds, namely triangulations for which every vertices form a face. (Triangulations of -manifolds with vertices must be -neighborly.) For this is essentially the Heawood conjecture. Ringel and Youngs showed, that 2-neighborly triangulation exists for all surfaces except for the Klein bottle. In dimensions greater than 2 only a small number of examples are known. Beside the triangulations that we talked about above, I am aware of two additional examples: In dimension 4: 16-vertex K3 surface (Casella-Kühnel 2001); In dimension 6: 13-vertex triangulations of (Frank H.Lutz).

Neighborliness is related to upper bound conjectures (that comes in various strengths) proposed by Kühnel in 1993. Here below is a lecture by Kuhnel in a birthday conference honoring the Indian mathematician Basudeb Datta. Kühnel’s conjecture for the maximum value of the Euler characteristic of a 2k-dimensional simplicial manifold on $latex n$ vertices

was settled by Isabella Novik and Ed Swartz in 2009. Novik and Swartz (for the orientable case) and Satoshi Murai (for the general case) also proved some strong forms of Kühnel’s conjecture conditioned on the Lefschetz property for the links; the Lefschetz property was proved by Karim Adiprasito in his -conjecture paper. (Things are moving along nicely in the -conjecture front (for older posts see here and here); I hope to write about it soon and in the meanwhile, here are two posts (I,II) by Karim.)

I also posed a related conjecture to the 1987 Brehm and Kühnel’s theorem. (Related to the 3ᵈ problem)

**Conjecture:** A polyhedral -manifold (more generally, a strongly regular CW manifold) in dimension *d* which is not a sphere has at least faces. (Including the empty face.)

We can expect that extremal cases are only in dimensions 2, 4, 8, and 16 and are projective plane like or even genuinly PL projective planes over the reals, complex, quaternions or octonions.

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Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left according to the outcome. Their coin flips create a simple random walk starting at the origin on the integers.

We know for sure that they we will return to the origin infinitely many times. However, their random walk never comes back to the origin, so we know for sure that one of them did not follow the rules!

## Test your intuition: Is it possible to figure out from the walk whether it was Ruth or Ron who did not follow the coin-flipping rule?

And the answer is **yes!** This is proved in the following paper:

Identifying the Deviator, by Noga Alon, Benjamin Gunby, Xiaoyu He, Eran Shmaya, and Eilon Solan

**Abstract:** A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases.

The paper gives a non-constructive proof for a strategy to identify the deviator and in the case of two-player random walk it gives an ingenious explicit identification method!

Here is a variant of the problem devoted to Itai Benjamini: Consider planar percolation on the rectangular grid. One player chooses every vertical edge with probability 1/2 and one player chooses every horizontal edge with probability 1/2. Lo and behold, there is an infinite open cluster. Can you (explicitely) detect the deviator?

]]>**Update**: fake reverse parking is known already as the much debated “pull-through parking”. (Thanks to Gali Weinstein over Facebook for telling me about it.) It is also mentioned as #879 among a thousand awesome things by Neil Pasricha.

When I was young my mother Carmela Kalai told me: “Always remember, Gili, how wonderful movies are and how happy I was to be born in the era of movies.” My father Hanoch Kalai told me: “Everything is interesting! Every subject, no matter how marginal and unimportant or boring it may look to you, Gil, when you study it in depth you will find it fascinating!”

One thing I tell my children is: “Remember the joy of fake reverse parking!”

Let me tell you in this post what fake reverse parking is:

The brief explanation is simple: when there are two (**unoccupied**) parking spaces, one after the other, you drive forward, pass one of the parking lots and locate your car in the second parking lot.

The general law about parking is this: forward parking is often easier than reverse parking but it is often harder afterwards to drive your car away. Reverse parking is harder than forward parking but later it is easier to get out and drive away. Fake reverse driving is easier than both and it is just as easy as ordinary reverse parking when it comes to leaving your parking place and driving away.

As you can see and feel by looking at the pictures, fake reverse parking is much easier than ordinary reverse parking and allows you to achieve the same results. As a matter of fact, fake reverse parking is even easier than ordinary forward parking.

**Ordinary forward parking**

Again, look at the three pictures above and witness for yourself how the pictures of ordinary reverse and ordinary forward parking can make you nervous, while the pictures of fake reverse parking evoke a calm and joyful mood!

Like many other joyous activities, some warnings are in place. In any kind of parking, it is a mistake to park your car in a parking place which is already occupied by another car. **For fake reverse parking make sure that there is no simultaneous attempt by another driver to park, using the ordinary reverse parking method inthe same parking space.**

One day I went with my youngest son Lior to some parking lot near Rehovot. (Here is a lovely post based on a question of Lior TYI38 Lior Kalai: Monty Hall Meets Survivor.) It was a large parking lot and it was completely empty. When I parked my son asked me “why didn’t you opt for fake reverse parking?” “Well”, I said “what I did is actually a ‘fake-fake reverse parking’. Later, when the parking space fills up, people will assume that I made a fake-reverse parking. But this was too easy with no cars around so my parking was actually a ‘fake-fake-reverse parking’, aimed at giving a feeling of fake reverse parking, while in reality it is not”. Lior, thought about it for a minute and then said: “Daddy, this is complete nonsense! There is no such thing as a ‘fake-fake reverse parking’. What you did is a simple reverse parking!”

“Well”, I thought, “it is good that my children are skeptical about things I tell them, and shoot down incorrect or silly ideas that I raise.” Moreover, quickly dismissing my idea about a “fake-fake reverse parking” strengthens the value of my classic idea about the importance and joy in ordinary fake reverse parking. Still, I was somewhat sad that my novel idea of fake-fake reverse parking was shot down so quickly. Maybe it has some deep meaning after all?

**an especially magical opportunity for fake reverse parking**

(Added August 18, 2022): Since the beginning of the corona pandemic I had a corner on this blog “to cheer you up in difficult times”. I must admit that I tried to cheer my audience up with silly, funny, and educating stories earlier on, but since the beginning of the pandemic which largely represented difficult times for all humanity that was not caused by human malice, I thought that these attempts have special value. Now, with the war in Ukraine, I decided to go back to the previous format were the value of being cheered up is left to your own judgement. This post #36 to cheer you up in difficult times is the last one.

]]>Science magazine has an article written by Adrian Cho Ordinary computers can beat Google’s quantum computer after all. It is about the remarkable progress in classical simulations of sampling task like those sampling tasks that led to the 2019 Google’s announcement of “quantum supremacy”. I reported about the breakthrough paper of Feng Pan and Pan Zhang in this post and there are updates in the post itself and the comment section about a variety of related works by several groups of researchers.

The very short summary is that by now classical algorithms are ten orders of magnitude faster than those used in the Google paper and hence the speed-up is ten orders of magnitude lower than Google’s fantastic claims. (The Google paper claims that their ultimate task that required 300 seconds for the quantum computer will require 10,000 years on a powerful supercomputers. with the new algorithms the task can be done in a matter of seconds.)

Also regarding the Google supremacy paper, my paper with Yosi Rinott and Tomer Shoham, Statistical Aspects of the Quantum Supremacy Demonstration, just appeared in “Statistical Science”. (Click on the link for the journal version.) The Google 2019 paper and, more generally, NISQ experiments raise various interesting statistical issues. (In addition, it is important to double check various statistical claims of the paper.) One of our findings is that there is a large gap between the empirical distribution and the Google noise model. I hope to devote some future post to our paper and to some further research we were doing.

The leaking of the Google paper in September 23, 2019 led to huge media and academic attention and many very enthusiastic reactions. I also wrote here on the blog a few critical posts about the Google claims.

Here is a figure with the price of bitcoin around the time of the Google quantum supremacy (unintended) announcement.

**Update**: There is a recent post on Shtetl Optimized with Scott Aaronson’s take on the supremacy situation. Overall our assessments are not very far apart. I don’t understand the claim: “If the experimentalists care enough, they could easily regain the quantum lead, at least for a couple more years, by (say) repeating random circuit sampling with 72 qubits rather than 53-60, and hopefully circuit depth of 30-40 rather than just 20-25.” In my view the most crucial task is to try to repeat and to improve some aspects of the Google experiment even for 20-40 qubits. (In any case, nothing is going to be easy.)

We know for sure that they we will return to the origin infinitely many times. However, their random walk never comes back to the origin, so we know for sure that one of them did not follow the rules!

In this post I would like to report on Kevin Buzzard’s spectacular lecture on moving mathematics toward formal mathematical proofs. (Here are the slides.) The picture above is based on images from the other spectacular Saturday morning lecture by Laure Saint-Raymond. The issues raised in Laure’s talk regarding fluctuations, atypical behavior, and chaos are rather close to my heart and recent interests.

Let me mention that in ICM2022 discord was used for question and answers (in addition, some of the lectures in front of live audience had a lovely Q/A part), and Kevin’s lecture led to many live questions and questions on discord.

**Kevin’s lecture gives strong evidence that the answer is yes!** Here is an analogy, until a few decades ago typing a paper usually involved handwriting it, giving it to a typist, and then making a few tedious rounds of corrections. This has changed and now most mathematicians type their own papers. It seems quite possible that in a couple of decades mathematicians will write their proofs in a way which allows automatic verification.

**Kevin Buzzard !**

Kevin demonstrated a verification of a proof to a theorem in topology asserting that the composition of two continuous functions is continuous. The demonstration was a little quick for me (I don’t know “Lean”) but it looked very convincing. You can see in real time how Lean replaces the term “continuous” with its definition and how the steps of the proofs enter Lean’s “brain”. Following this demonstration Kevin also showed a couple of short-cuts, using so-called “tactics” based on tricks or facts that the program already know. (The second short-cut was based on the theorem already there in the library.) At the end of each proof the program asserts “goals accomplished” with an emoji of a flower.

Proving theorems, Kevin said, turns into a nice computer game. Kevin also described the prehistory; indeed the example above could been achieved by systems from the 90s.

This was the main part of Kevin’s lecture and the progress is mind-boggling.

2004: A formal proof of the prime number theorem (Avigad et al using “Isabelle/HOL”, not having complex analysis it verified an elementary proof.) In 2009 Harrison verified the complex analysis proof.

2004: Gonthier formally verified the four-color theorem (using “Coq”)

2005: Hales verified the Jordan curve theorem (“Isabelle/HOL”)

2013: Gonthier et al formally verified Feit and Thompson’s odd order theorem

**###**

2015: Hales and a team found a formalized proof for the Kepler conjecture (that he and Furgeson had proved in 1998). Hales’ 2017 lecture on this proof changed Kevin’s life and led him to his work on formal proofs. Hales proposed to create a system capable of “understanding” all statements of theorems published in serious mathematical journals. (Understanding statements is easier than understanding proofs.)

First, Kevin said, one needs to formalize all the statements of undergraduate mathematics.

**###**

In 2017 Kevin started a Lean club for undergraduates! They did very well. The lean community (I suppose Lean is used for other things) embraced this project.

Introduced by Grothendieck in 1960, schemes made understandable to computers by Lean in 2018. (Schemes and especially schemes of line-bundles are needed for understanding Kazhdan’s lecture from the previous post. I personally have a vague understanding of what they are. BTW, the lecture mentions Scott Morrison as a Lean star and I wondered if this is the MathOverflow star by the same name.)

**###**

Next, Kevin mentioned the progress related to Scholze’s perfectoid spaces. Earlier, very complicated proofs to simple-to-state theorems were formalized and this was a formalization of very simple theorems on very complex objects. It was also a nice way to learn the definition!

**&&&**

Lean and even its mathematical library “mathlib” are by now gigantic project and Kevin made it clear that it’s not “his” project but rather that he is one of many, many participants.

2020: The Scholze challenge (we talked about it in this post, and in any case it is way over my head). This is an example of formalizing a very complex proof of a very complex theorem. It eventually led to a somewhat different proof and better understanding of the necessary underlying objects.

2018: A new proof by Gouezel and Shchur for a 2013 theorem by Shchur whose formalization led to finding an error and then correcting it.

2019 the proof of the 2016 cap set conjectures (see this post) was formalized.

2021 Bloom proved that every dense set of integers contains a finite subset where the sum of reciprocals equals 1. The proof was formalized by Bloom and Bhavik Mehta (including all earlier results the paper relies on and including the circle method).

2019 Apery’s proof of the irrationality of zeta (3) was formalized.

Let me stop here, there were 20-30 more startling successes for which I refer you to the talk itself. Fermat’s last theorem, Poincare’s conjectures in dimensions 4 and 3 and the classification of finite simple groups are still waiting for their turn and of course so are many more less famous proofs. Kevin refers to it as a new era of digitizing mathematics.

Kevin complained about this matter (every appearance of **###** above) but I tend to disagree with this complaint. Formal proofs did gain a lot of attention and, in any case, the appropriate response if you do not get attention is “to work harder” which incidentally is also (on the nose) the appropriate response if you do get attention. Also, Robert Aumann often says that in science, like in other areas, salesmanship accounts for more than 50% of success, and indeed Kevin mentioned that salesmanship was among the motivations of one of their projects (**&&&** above).

The lecture mentioned a single case for which the proof was corrected. It will be surprising (perhaps even suspicious) if upon formalization, 99% of proofs turn out to be correct. (And there are interesting issues on what to do with theorems and proofs that we cannot verify formally.)

This is something I asked about in discord and it led to interesting comments. (It is related to the previous question.) Kevin mentioned, for example, that initially the proof of the irrationality of zeta (3) proved a different statement.

Probably, yes! This is an interesting issue worthy of further discussion.

This is also something I asked about over discord. I was referred to the following link: Combinatorics in lean.

I suppose that the answer is positive. This would be a nice project.

This does not seem out of the question, but having such a “compiler” will require also different AI abilities that go well beyond current efforts.

Kevin started his lecture by answering “NO” and referring to such a possibility as “science fiction”. The way I see it is that there are various avenues towards computerizing (what we regard now as) the creative process of mathematics including coming up with conjectures, proving theorems, and building theories, and formalizing mathematical theorems and proofs besides its own value can also be regarded as an avenue (among several) in automatizing mathematics.

Kevin asserted that he is not impressed by current successes, but people could equally be unimpressed with formalizing mathematics in 2010, and he mentioned some reasoning coming from AI for why it is difficult (which I could not understand). On the other hand, since he regarded the state of the project as “the beginning of the beginning” it may be the case that Kevin does think about tasks which go beyond “just” formalizing mathematics.

There are various other skeptical voices regarding the possibility of replacing humans with computers in mathematical research, including the famous mathematician Michael Harris who often writes about it, but I am not familiar with the skeptical arguments themselves.

There are many people who are enthusiastic about replacing humans with computers in doing mathematics and few of them even put their careers where their mouth is. Doron Zeilberger (aka, Doron Z. and Dr. Z) is a very famous example. Now, with the next 2026 ICM in Philadelphia, we can say that:

If Doron Z. does not come to the ICM, the ICM comes (pretty close) to Doron Z,

and it will be nice to see various aspects regarding the interface between mathematics and computers represented in ICM 2026.

Regarding the use of computers in major mathematical *achievements* see these two Math Overflow questions (one, two).

Another link from the discussion: Solving (Some) Formal Math Olympiad Problems

**A description of a Lean project in progress. The green ellipses represent completed parts. I am a little worried by the ellipse where it is written “clearly” and also by the one with the title “it is easy to see”** .

Updates:

1) Doron Zeilberger, a pioneer in using computers for mathematics, wrote a skeptical opinion regarding the formal proof direction https://sites.math.rutgers.edu/~zeilberg/Opinion184.html . Twelve years ago he wrote a similar opinion .

2) Georges Gonthier, an early hero on formal proofs gave another ICM 2022 lecture: Computer proofs: teaching computers mathematics, and conversely.

]]>ICM 2022 is running virtually and you can already watch all the videos of past lectures at the IMU You-Tube channel, and probably even if you are not among the 7,000 registered participants you can see them “live” on You-Tube in the assigned date and hour.

I landed back from Helsinki on Wednesday night and I devoted Thursday to watch lectures, while in later days other tasks and obligations gradually took over part of my time. I plan to catch up during the summer.

The three plenary lectures on Thursday, July 7 were around the **Langlands program**.

All three plenary lectures on Thursday were about the Langlands program. The opening lecture by my friend and colleague David Kazhdan proposed, mainly to experts in representation theory, a glance **well beyond the horizon**. David offered three complementary approaches to a far-reaching extension of the Langlands program where one attempts to replace “global fields” by more general fields. Specifically, David and his collaborators want to extend the unramified Langlands correspondence from fields of rational functions on curves over **finite fields** to fields of rational functions on curves over **local fields**. The ICM lecture was rather short, however, David gave two detailed talks at our basic notion seminar and here is the recording of the first lecture.

**David Kazhdan’s lecture in our basic notion seminar**

Marie-France Vignéras and Frank Calegari gave wonderful general audience lectures. Marie-France even advised the experts in the lecture room to consider going somewhere else, and Frank posted his amazing mathematical video on his blog, adding a disclaimer that the target audience for his blog is close to orthogonal to the target audience for his talk.

**Pictures from Calegari’s lecture: Some computations from Frank Calegari’s lecture may appeal to very large audiences (top left); Later things get more difficult: A recent breakthrough by Ana Caraiani and Peter Scholze (Caraiani also gave an ICM lecture) is mentioned and so is the recent proof of the Hasse-Weil conjecture for surfaces of genus 2!**

**Pictures from Marie-France Vignéras’ lecture.**

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I am writing from Helsinki where I attended the meeting of the General Assembly of the IMU and yesterday I took part in the moving award ceremonies of ICM2022 hosted by Aalto University. This will be the first post about the ICM 2020 award ceremonies.

The opening day of ICM2022 was exciting. Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska were awarded the Fields Medals 2022. Mark Braverman was awarded the Abacus Medal. The event was videotaped and can be found here. **Update**: The five lectures of the medalists can be found here.

In the ceremony, I gave the laudation for June Huh. Here are the slides of my talk. The preliminary version of my proceeding paper is here on the IMU site. Please alert me about mistakes in my paper or if you have any suggestions for changes or additions. (I already found that on two occasions I embarrassingly wrote “Brändén” Instead of “Braden”, sorry for that.) **Update:** Here is a corrected version.

The IMU site contains a lot of material about the Fields medalist and other prize winners. It contains beautiful videos, and preliminary versions of the proceeding papers by the medalists and by those giving the laudations.

Andrei Okounkov wrote four wonderful detailed “popular scientific expositions” (those are available on the IMU site) which provide much scientific background as well as Andrei’s own scientific perspective. It is a great read for wide audience of mathematicians, ranging from advanced undergraduate students. Experts will also enjoy Andrei’s perspective.

I hope to discuss these awards and some further personal and mathematical reflections in a subsequent post.

Let me give some links to discussions here on the blog on works by laureates.

I wrote about Maryna Viazovska’s amazing breakthrough in the post A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24, and this additional post Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska: Universal optimality of the E8 and Leech lattices and interpolation formulas.

I reported here in 2009 on the startling solution by Mark Braverman of the Linial-Nisan conjecture.

The story of James Maynard’s startling results and the gap between primes story is described in this post. In July 2014 we ran at HUJI a beautiful learning seminar on small gaps between primes, where James Maynard gave a series of three lectures. His result on “bounded intervals containing many primes” both strengthened and simplified Yitang Zhang’s earlier amazing result on “bounded intervals containing two primes.” Maynard developed large chunks of his approach independently from Zhang’s work.

I discussed two results by Hugo Duminil-Copin : After the start of the pandemic but before the war in Ukraine, I had a “cheer-you-up in difficult times” corner and in this post, to cheer you up, I wrote about a breakthrough by Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu, Mendes Oulamara (and yet another wonderful result by Hugo Vanneuville and Vincent Tasion). In this 2015 post I wrote about another breakthrough by Hugo Duminil-Copinand Vincent Tasion. (And see this post for a picture of Hugo mentioning KKL and BKKKL.)

And, of course, I wrote about June Huh several times. Here are a few examples: About Huh’s 2018 ICM talk; ICM 2018 Rio (4): Huh; Balog & Morris; Wormald; about the Mihail-vazirani conjecture Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant Solved the Mihail-Vazirani Conjecture for Matroids! ; About the early works on the Heron-Rota-Welsh conjecture for representable matroids; and about the full solution of the Heron-Rota-Welsh conjecture by Adiprasito, Huh, and Katz.

In this post we tried to cheer you up with “harmonic polytope”, which came up in Ardila, Denham, and Huh’s work on the Lagrangian geometry of matroids and were further studied by Federico Ardila and Laura Escobar.

]]>Next Tuesday, July 5 2022 will be the opening day of the International Congress of Mathematicians (ICM 2022) that, because of the war in Ukraine, will be fully virtual. Here is the link for the program for ICM 2022 according to days. For those who did not register or who want to hear several parallel talks the organizers promised to release all videotaped lectures shortly after the end of the congress. The IMU Award Ceremony 2022 on 5 July will be streamed live from Helsinki via the IMU’s YouTube channel and Facebook page.

Here is the website of ICM 2022. Here is a very useful webpage of supporting satellite events. One of those events take place at HUJI.

Between July 3-8, 2022 we will have a “Dynamics Week” in Jerusalem which will consist of two related but separate conferences at the Mathematics Institute of the Hebrew University. The first conference is **Ergodic Theory and Beyond**, July 3-5, emphasizing the connections between ergodic theory and other fields celebrating Benjy Weiss’s 81st birthday (originally planned to celebrate his 80th but then the pandemic happened). The second conference is **in person session of the virtual ICM**, July 6-8, with speakers mostly (but not only) from the dynamics section.

Today, June 26 2022, is the opening day of Algorithmic Game Theory: Past, Present, and Future, a workshop in honor of Noam Nisan’s 60th Birthday. The workshop takes place on June 26-30 2022, at the CS building at The Hebrew University of Jerusalem. Noam is a long time friend and colleague and I am proud to say that I was his second year linear algebra TA in the late 70s. Noam is also among the people that suggested to me to start a blog and he opened his own (now collective) blog a short time later. Congratulations, Noam!

Two other legendary computer scientists of the same early 1960s vintage also had birthday conferences. 40 Years of Distributed Computing was a workshop celebrating Hagit Attiya’s 60th birthday, and there was a half-secret conference celebrating Moni Naor’s birthday that I could not find on the internet. Congratulations Hagit and Moni!

I was happy to learn last week (English) about ten newly elected members, five women and five men, to the Israel Academy of Sciences and Humanities. Among them, Noam Nisan. Congratulations to all new members, and to the Israeli academy.

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