Monday, January 10,2022 10:00-16:00 (Israel time)

While at the Rio conference, I met, for the first time, quite a few people including the (then) current and previous IMU president Shigefumi Mori and Ingrid Daubechies, and the current IMU secretary Holge Holdem. I went mainly to the combinatorics and TCS sessions. The highlight of the opening ceremony that I watched with Itai Benjamini and Tammy Ziegler in Tel Aviv was the announcements of Field-medal recipients, and I enjoyed also when Mori recounted his first ICM where he had been awarded the Fields medal and how nervous he was.

So the plan for this post is as follows: I will share with you some memories of Assaf, whom I know since he was an undergraduate student at HUJI, and will then proceed to tell you about the three ICM plenary talks of Christian, Geordie, and Assaf.

I have known Assaf since he was an undergraduate student at HUJI. He took my first year course on discrete mathematics, and he told me an amusing story about it.

The lecture took place in “Canada lecture hall” where there were four rolling blackboards, each divided into 12 or so rectangular parts that I will call “blackboardettes”. Once I finished writing on some of the small blackboardettes, I had the habit of moving on to a completely random new one. The students found it frustrating since they could not trace back to the previous blackboardette. So one day I came to class and saw that the students numbered the blackboardettes from 1 to 48 in a random way. The students respected my disposition of writing on the blackboard in a completely unorganized way but they still wanted to be able to trace back. When I saw the numbering, I immediately realized the intention (or so Assaf says), I complied with the numbering, and the students were pleased about it.

The next memory about Assaf and me was from a really great conference at Edinburgh in the early 2000s. It was one of two conferences, where I came with a large delegation of seven members: my wife and children and also my mother and sister. We were all living in some dormitories and the lectures were a 15-minute walk away. One morning Assaf and I somehow went there after the main group of mathematicians, Assaf followed me to the location of the lectures, we pleasantly chatted about various things, and after 45 minutes he asked me if I knew where I was going and my response was “no”. (But somehow we got there, eventually.) You can read some India mathematical memories about Assaf in this post.

Let me make a small diversion and mention the other conference which I attended with a delegation of the same seven members, my wife and children, mother and sister. The conference took place in 1997 in a town Sant Feliu de Guíxols a little north of Barcelona in Catalonia, Spain. The main organizer was Anders Björner and it was essentially a highly successful union of several sub-conferences on several areas of combinatorics. One day we went to tour a picturesque town nearby and I found myself at the head of the group talking with a colleague, and behind me was a long line of 100 or so participants and a few family members. At some point I discovered that the path of mathematicians crossed itself! like this

and still people obediently followed with no shortcuts! I think that my path with Assaf in Edinburgh was at least a self-avoiding walk, but I cannot swear that this was indeed the case.

Before reaching out to my lecture notes I would like to share with you one thing that I have learned and still remember: You have to adopt the numerical methods to the deep structures of the problem. The law for the numeric is the same as the law for the system. (Another way to say it is: a good algorithm should respect the structure of the problem). This reminds me of something important about noise: that often, the noise respects the same laws as the system. Numerical approximation for mathematical systems seems similar in spirit to real-life approximation of (or by) mathematical systems. Another way to think about it is as follows: you have an ideal mathematical system say a PDE. Now, on the one hand you want to think about real life systems that are ideally described by this PDE. On the other hand, you want to think about numerical schemes that approximate the PDE. Maybe these two are two sides of the same coin.

Now, said Christian, the structure of the problem often refers to geometry. So this brought geometry into the problem and led to the theory of geometric numerical integration. And the systems considered in the lecture were Hamiltonian systems.

The lecture moved on from Hamiltonian ordinary differential equations to multi scale Hamiltonian systems to Hamiltonian PDEs, then considered low rank approximation and concluded with quantum systems. And when you hear the lecture you feel that you understand these concepts; everything is gentle and friendly. I will mention one more thing: the Euler numerical method was introduced 250 years before the lecture. And Christian mentioned one system – the solar system. (He showed a picture that still included Plato.) He explained why the symplectic version of Euler’s method is appropriate, and then moved on to discuss **numerical evidence that the solar system is chaotic**. OK I will stop here and leave out many exciting punchlines and details. For much more, watch the video!

Sometimes when talk number **k** in a conference is incomprehensible or when I don’t enjoy it for any other reason I skip talk number **k+1** . (I know this is neither so fair nor rational.) Usually, when I hear a good talk I have a greater passion for hearing the next talk. But on Wednesday morning I was so overwhelmed by the great performances of Geordie, and Assaf that I could not stay for another talk. Instead, I only saw the videotaped lecture a few weeks later. The best way for that, I found out, was while babysitting my grandchildren in the evenings when my daughter Neta and her husband Eran went out to a restaurant or a movie and Ilan and Yoav were sleeping. (I could see there the lecture on their TV which was directly connected to a computer.) For a few months after the ICM, I saw the video in four overlapping parts and I greatly enjoyed it. (and also Eran and Neta enjoyed my volunteering.) Lubich’s lecture was also a great lecture, and I am sure that the live version was even greater. I got very excited by the topic and some of the major insights.

Christian talked about numerical methods and approximations and I thought about noise which I like, and this reminded me of the saying that if you if you have a hammer you treat everything as if it were a nail.

Indeed, it occurred to me recently that the famous description of treating everything as nails if you have a hammer, is more obliging than demeaning. In my view, it is a good thing to think about matters in the lens of your tools, even for the purpose of reaching to other areas and eventually adopting other tools.

One great conjecture that I had been hearing about since the 1980s is the conjecture that the Kazhdan-Lusztig polynomials have non-negative coefficients for all Coxeter groups. The case of Weil groups was proved by Kazhdan and Lusztig in the late 1970s. In 2012 David Kazhdan gave a class about the startling solution of Elias and Williamson to the Kazhdan-Lusztig conjecture for general Coxeter groups. (The class mainly described Soergel’s program for solving the conjecture.) Later, I first met Geordie in person at the Berlin 2016 European Congress of Mathematics. Here is a great talk by Geordie on representation theory and geometry.

A) Groups and representations: a quick explanation of representation theory.

The idea is that groups in mathematics are everywhere, groups are complicated nonlinear objects, and representation theory is an attempt to “linearize” groups, thus studying simpler objects and then drawing conclusions for groups.

Geordie’s first example was the group of symmetries of the icosahedron which is also a group of isometries (represented by matrices) of ,

Why study representations? Geordie first mentioned the symmetric group (which is related to later parts of the talk, and to a lot of combinatorics) and Galois representations (which are related to various other talks in the conference).

Next came the notions of simple and semi simple representations followed by an example of a representation that is not semi-simple but still has some structure that resembles semi-simplicity.

B) The semi-simple world; how geometry enters the picture, and how algebraic arguments can replace geometric arguments.

Two fundamental theorems are:

Maschke 1897: every representation of a finite group is semi-simple.

The proof (which was given in the lecture!) explains how geometry enters the story.

Weyl 1925: every representation of compact Lie group is semi-simple.

C) Beyond semi-simple representations: Kazhdan-Lusztig theory.

Geordie talked about the group as a guide for going beyond compact lie groups and semisimplicity. A bit later toward the Kazhdan-Lusztig theory he talked about (It should be caligraphic sl, I suppose), namely complex matrices with trace 0. He then proceeded to describe the Verma modules which play a central role in the story and the Kazhdan-Lusztig conjecture regarding the description of the representation on the Verma modules. He explained that orthogonality and direct-sum structures for the compact Lie group theory was replaced by certain “canonical basis” and filtrations for algebraic structures beyond semi-simplicity. The Kazhdan-Lusztig conjecture was settled shortly after it was posed using geometric tools along with a related conjecture by Jantzen. It took almost four decades for algebraic proofs (which gives plenty more) to be found.

D) Shadows of Hodge theory: Soergel’s program, Elias-Williamson’s algebraic proof for Kazhdan-Lusztig conjecture (and the positivity conjecture); and various other conjectures.

Geordie mentioned that his proof with Elias gives a sort of shadow of Hodge theory in cases where algebraic varieties do not exist and mentioned other cases where shadows of Hodge theory are known and expected. This is also related to June Huh’s lecture that we discussed in this post.

E) Modular representations, Lusztig’s new character formula, and the billiard conjecture

While the representation theory of the symmetric group over the complex numbers is a well developed theory, once you move to finite fields our knowledge is considerably lower. Geordie described some results and conjectures in this direction.

This reminds me that in the early nineties, Micky Ajtai was interested in applications of modular representation of for computational complexity theory.

What did Cartan write to Weyl? In what year was the first algebraic proof of the Weyl theorem discovered? What was the role of Kasimir? How does Verma fit the picture? and Harish-Chandra? And why was the Kazhdan-Lusztig theory revolutionary? For all this and more, watch the video!

For this talk, like the other preceding talks, the interplay between linear and non-linear objects is an important theme.

The “Ribe program” is an attempt to organize the vast world of metric spaces. Metric spaces have many connections within mathematics, pure and applied, and connections to theoretical computer science, as well as other sciences. Special cases of metric spaces which originally motivated Martin Ribe are metrics described by normed spaces, and for them there is an important well-developed theory. Ribe discovered that many properties of normed spaces are “metric properties in disguise”, and this gives an opportunity to extend notions and results from the theory of Banach spaces to general metric spaces; Spanning several decades, this program have now become a large theory. (Normed metric spaces are described by their unit balls which are centrally symmetric convex sets that we like here on the blog.) General metric spaces are much more general objects than normed spaces, and it looks like a rather wild idea that insights about normed metric spaces extend to metric spaces described by Riemannian manifolds, complicated molecules, or by the connection-graph of the internet. Assaf mentioned Jean Bourgain and Joram Lindenstrauss as having pioneering roles.

“Dimension reduction” is also a very important paradigm common to many mathematical and scientific disciplines. The question is of finding useful ways of representing high dimensional data in low dimensions. Much of Assaf’s talk was devoted to dimension reduction within the Ribe program.

A very general framework is the question: When can you find a metric space inside a class of metric spaces, where “find” can refer to various notions of embeddability. Among the opening examples of a theorem in this direction, Assaf mentioned the existence of metric spaces proved by him with Eskenazis and Mendel, that you cannot “find” even in a very weak sense in any spaces of nonpositive curvature.

Johnson-Lindenstraus: Any billion vectors in a billion-dimensional vector space can be realized in 329 dimensions with distortion at most 2!

(In general, to get a constant distortion you can go (and need to go) to dimension.)

What happens when you start with an arbitrary metric space of n elements? Can you embed it in some log *n*-dimensional normed space? Assaf gave a proof based on volumes for why you cannot go below log *n*. Next came a result by Bourgain that showed that dimensions are necessary. Some years later Linial, London and Rabinovich showed that are required, and a breakthrough 1996 result by Matoušek who showed that you need dimensions for some ! Twenty years later, in 2016, Naor proved that -dimensions are required even for a much weaker form of embedding where the distortion is taken on average.

Toward the end of the proof Assaf defined a generalized notion of expanders: Ordinary expanders correspond to the -norm and there are analogous definitions for every norm.

Again, for much more, watch the video.

Our gifted columnist Alef has updated his ICM2022 drawing; he added a bit of the St. Petersburg skyline and diversified the participants. Here it is.

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What will be the next term in the sequence **AGC-GTC-TGC-GTC-TGC-GAC-GATC- ???**

**GTC****GATC****TAGC****GCTC****C:GAT**- Another answer

Oberwolfach, Geometric, algebraic and topological combinatorics, 2019. Giulia Codenotti, Aldo Conca, Sandra Di Rocco, Bruno Benedetti, and Lorenzo Venturello

At the end of August 2019 we had in Oberwolfach a very fruitful meeting on Geometric, algebraic, and topological combinatorics. (In this post, I mentioned an open problem from the problem session.) I came to Oberwolfach just after a visit, with my son-in-law, Eran, to CERN near Genève. (See this post for pictures from ATLAS, CERN, and this post regarding my CERN colloquium.)

The August 2019 Oberwolfach meeting was the seventh meeting in a series of meetings that started in 1995. Here is, by the way, is very nice article in Quanta Magazine about an Oberwolfach Meeting. (And feel free to share Oberwolfach memories in the comment section.)

The sequence in the title of the post is not a DNA sequence or something similar but rather it refers to these meetings in Oberwolfach and this post is devoted to these series of meetings and other meetings in Oberwolfach.

Here A stands for ‘Algebraic’, G stands for ‘Geometric’, T stands for ‘Topological’ and C stands for ‘Combinatorics’.

These series of conferences are devoted to algebraic, geometric, and topological combinatorics. Both algebraic and geometric combinatorics are very large areas (and topological combinatorics is pretty large) and usually participants of the conference are divided into several overlapping, much appreciated minorities. Actually, living in a country where every citizen is a member of a much appreciated minority seems like a nice political setting to me.

Here is the review of the first conference in the series AGC95.

I was slightly younger than 40 years old. The meeting, organized by Anders Björner, Günter Ziegler and me, took place before a sabbatical semester at IAS, Princeton in the fall 1995. Here are a few topics that were discussed:

**Cluster algebras to be.** Sergey Fomin’s lecture was on Piecewise-linear maps, total positivity, and pseudoline arrangements, it represented a joint work with Arkady Bernstein and Andrei Zelevinsky. This paper was the starting point of vastly influential cluster algebras that Sergey, Arkady, and Andrei started developing around that time.

**Polytopes spheres and face numbers.** Tom Braden talked about Intersection homology and polytopes – recent progress, this was about his paper with Bob MacPherson where (among other things) a conjecture that I made some years earlier was settled.

**Convexity in the Grassmannian.** Eli Goodman talked about a joint work with Ricky Pollack on some combinatorial questions for convex sets on affine Grassmanian. Finding the right notion of convexity for a subset of the Grassmannian is a fascinating and unexplored question.

**Optimization.** Monique Laurent talked about the geometry of the set of positive semidefinite matrices with diagonal entries. Rekha Thomas talked about using Gröbner bases to solve integer programs (and a comparison between linear and integer programming).

**The two 2-lecture series. **Nati Linial gave a series of two lectures on **the geometry of graphs**. He talked about his program to think about graphs as metric objects and apply insights regarding metric spaces to theoretical computer science. This was shortly after the Linial-London Rabinovich paper that had large impact in theoretical computer science and combinatorics had appeared. Rade Zivaleivich gave two lectures on methods of obstruction theory, related to topological and colorful Tverberg theorems and measure partitions and other questions. We came back to this topic in subsequent conferences in the series.

**Real algebraic geometry.** Ricky Pollack talked about Complexity and algorithms in real algebraic geometry.

**Triangulations of cyclic polytopes and the generalized Baues Conjecture**.

Jorg Rambau talked about a counterexample to the “Generalized Baues Conjecture” and Vic Reiner talked about Triangulations of cyclic polytopes: the higher Stasheff-Tamari posets.

**Universality. **Jürgen Richter Gebert explained why Realization spaces of 4-polytopes are universal!

See the review for some more talks on the topics listed above and on other topics such as **Lattices of parabolic subgroups, ****Discrepancy theory, ****Combinatorics of knots **and more**.**

Here are links to the workshop pages (WP) and full reviews (FR) of AGC, 1995 (WP, FR) ; GTC, 1999 (WP, FR); TGC, 2003 (WP, FR); GTC, 2007 (WP, FR); TGC, 2011 (WP, FR); GAC, 2015 (WP, FR); and GATC, 2019 (WP, FR).

**Flashback: my first meeting at Oberwolfach**

I was a 27 year old graduate student. It was just after the 1982 Lebanon war. I had a one year old daughter and following the meeting my wife and I toured Italy for a week. It was great! My thesis supervisor Micha A. Perles and my academic brother Michael Kallay also participated. At that conference I met for the first time many mathematicians and some of them have remained my good friends ever since. The meetings on Konvexe Körper took place every two years and I participated in several subsequent meetings.

The other series of conferences in Oberwolfach that I attended regularly, is the combinatorics meeting that takes place in the first week of January every 2-3 years. The first one in the series was also the first Oberwolfach meeting after 2000. The last meeting in this series was in January 2020 and just before the meeting my wife and I spent four great days in Rome. This was in fact our last trip outside Israel until September 2021 (not counting a 1-day visit to Petra).

Half a year ago Isabella Novik, Paco Santos, Volkmar Welker and I submitted a proposal for a 2023 meeting which is going to be the 8th meeting in this series. Recently the meeting was approved! It will take place on December 10-16, 2023.

Useful links: Oberwolfach; Oberwolfach photo collection; List of workshops since 1949;

]]>Richard Stanley, a most famous and influential mathematician in my area of combinatorics, the master of finding deep connections between combinatorics and other areas of pure mathematics, and my postdoctoral advisor, has just won the Steele prize for lifetime achievement, among the most prestigious mathematical prizes.

The citation reads: “Stanley has revolutionized enumerative combinatorics, revealing deep connections with other branches of mathematics, such as commutative algebra, topology, algebraic geometry, probability, convex geometry, and representation theory. In doing so, he solved important longstanding combinatorial problems, often reinvigorating these other fields with new combinatorial methods. Through his outstanding research; excellent expository works; and many PhD students, collaborators and colleagues, he continues to influence the field of combinatorics worldwide.”

Congratulations to Richard and to the community of combinatorics.

Richard’s work is mentioned in many posts over my blog but let me point you specifically to:

The post Happy Birthday Richard Stanley! describes seven early papers by Richard Stanley that you must read!

Richard Stanley’s work is mentioned in these posts (among more) that are related to the upper bound theorem and the g-conjecture. (Eran Nevo) The g-conjecture II: The commutative algebra connection,); (Eran Nevo) The g-conjecture I, and How the g-conjecture came about ; Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found; Beyond the g-conjecture – algebraic combinatorics of cellular spaces I; Open problem session of HUJI-COMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem; Amazing: Karim Adiprasito proved the g-conjecture for spheres!; Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.

Additional posts:

A Mysterious Duality Relation for 4-dimensional Polytopes.

Around the Garsia-Stanley’s Partitioning Conjecture

To cheer you up in difficult times 10: Noam Elkies’ Piano Improvisations and more;

(1) Richard drove cross-country at least 8 times (2) In his youth, at a wild party, Richard Stanley found a proof of FLT consisting of a few mathematical symbols. (3) Richard jumped at least once from an airplane (4) Richard is actively interested in the study of **consciousness** (5) Richard found a mathematical way to divide by zero

**Answer: All five statement above are correct! **

A few hours ago the first issue of *Combinatorial Theory* was published. I am happy and proud to take part in this new endeavor. The editorial speaks for itself.

This is the first issue of our new journal,Combinatorial Theory. It is owned by mathematicians, dedicated to Diamond Open Access publishing with no fees for authors or readers, and committed to an inclusive view of the vibrant worldwide community in Combinatorics. The journal shares a similar scope with the long-runningJournal of Combinatorial Theory Ser. A(JCT A), owned by Elsevier. In 2020, almost all of the editors of JCT A resigned, deciding that it was the time to found a premier Combinatorics journal owned by mathematicians, not by a commercial publisher. Thus was bornCombinatorial Theory. That birth has allowed us to rethink how and what we publish. We are proud to have assembled a broad and diverse team of editors. We are also pleased with two new features in our editorial process:doubly-anonymous refereeingto mitigate implicit biases during peer review, and the inauguration ofExpository Articlesubmissions to encourage inclusion of valuable well-written expositions.

I also have warm feelings toward *Journal of Combinatorial Theory Ser. A* and the earlier *Journal of Combinatorial Theory* (before it split to Ser A and Ser B), which was among the first journals of combinatorics, had important role for the development of our field, and which is still running under new editors.

Consider a finite family of circles such that every point in the plane is included in at most two circles. What is the minimum number of colors needed to color the circles so that tangent circles are colored with different colors?

**Ringel 1959 circle problem** is the question if this minimum number of colors is bounded.

I mentioned the problem in a post about eight coloring problems for arrangements of circles and pseudocircles, three years ago. (For another recently solved conjecture by Ringel see this post.)

In a recent arXiv paper James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak solved the problem and showed that any finite number of colors does not suffices. In fact the proved considerably more. The paper is

and here is the abstract

**Abstract:** We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel’s circle problem (1959). The proof relies on a (multidimensional) version of Gallai’s theorem with polynomial constraints, which we derive from the Hales-Jewett theorem and which may be of independent interest.

Congratulations to the authors.

]]>And a Quanta Magazine article about it.

This paper deals also with quantum codes (see this post). Pavel and Gleb are also responsible (with Man-Hong Yung) to a recent breakthrough regarding classical simulations of random quantum circuits mentioned in this paper. (See this comment.)

Update (Jan. 8, 2022): And a Quanta Magazine article about it.

This paper described related constructions and posed some conjectures settled in 2.

]]>One of the exciting directions regarding applications of computers in mathematics is to use them to experimentally form new conjectures. Google’s DeepMind launched an endeavor for using machine learning (and deep learning in particular) for finding conjectures based on data. Two recent outcomes are toward the Dyer-Lusztig conjecture (Charles Blundell, Lars Buesing, Alex Davies, Petar Veličković, Geordie Williamson) and for certain new invariants in knot theory (Alex Davies, András Juhász, Marc Lackenby, Nenad Tomasev). There is also a Nature article Advancing mathematics by guiding human intuition with AI, on these developements. Here are also links to a new MO question and an old one on applications of computers to mathematics.

In a post on the “G-programme” I mentioned the Dyer-Lusztig conjecture (Problem 11) and a much much more general fantasy (Problem 12), So let me quote this part of the post here.

What happens when you give up also the lattice property? For Bruhat intervals of affine Coxeter groups the Kazhdan Luztig polynomial can be seen as subtle extension of the toric g-vectors adding additional layers of complexity. Of course, historically Kazhdan-Lusztig polynomials came before the toric g-vectors. (This time I will not repeat the definition and refer the readers to the original paper by Kazhdan and Lusztig, this paper by Dyer and this paper by Brenti. Caselli, and ^{ }Marietti.) It is known that for Bruhat intervals with the lattice property the KL-polynomial coincide with the toric *g*-vector. Can one define h-vectors for more general regular CW spheres?

**Problem (fantasy) 12:** Extend the Kazhdan-Luztig polynomials (and show positivity of the coefficients) to all or to a large class of regular CW spheres.

This is a good fantasy with a caveat: It is not even known that KL-polynomials depend just on the regular CW sphere described by the Bruhat interval. This is a well known conjecture on its own.** (This is the Dyer-Lusztig conjecture.)**

**Problem 11:** Prove that Kazhdan-Lustig polynomials are invariants of the regular CW-sphere described by the Bruhat interval.

A more famous conjecture was to prove that the coefficients of KL-polynomials are non negative for all Bruhat intervals and not only in cases where one can apply intersection homology of Schubert varieties associated with Weil groups. (This is analogous to moving from rational polytopes to general polytopes.) In a major 2012 breakthrough, this has been proved by Ben Elias and Geordie Williamson following a program initiated by Wolfgang Soergel.

]]>**The logarithmic origin of ****Manhattan**

We are spending the fall semester in NYC at NYU and yesterday* I went to lunch with two old friends Deane Yang and Gaoyong Zhang. They told me about the logarithmic Minkowski problem, presented in the paper The logarithmic Minkowski problem by Károly Böröczky, Erwin Lutwak, Deane Yang and Gaoyong Zhang (BLYZ). (See also this paper by BLYZ.) We will get to the problem after a short reminder of Minkowski’s theorem.

**The Discrete Minkowski problem:** Find necessary and sufficient conditions on a set

of unit vectors in and a set of real numbers that will guarantee the existence of an -faced polytope in whose faces have outer unit normals and corresponding face-areas .

Minkowski himself gave a complete solution in 1911, a necessary and sufficient condition is that the following relation holds:

.

If a polytope contains the origin in its interior, then the cone-volume

associated with a face of the polytope is the volume of the convex hull of the face

and the origin.

**The Discrete logarithmic Minkowski problem:** Find necessary and sufficient conditions on a set

of unit vectors in and a set of real numbers that will guarantee the existence of an -faced polytope in whose faces have outer unit normals and corresponding cone-volumes .

The problem was solved by BLYZ for the centrally symmetric case. It is related to a lot of deep mathematics (convexity, valuations, Brunn-Minkowski theory, analysis, PDE… perhaps combinatorics). In both cases there are continuous versions that are a little harder to formulate.

**With Deane Yang and Gaoyong Zhang**

* Actually it was four weeks ago and since then we had another lunch and Deane explained some recent issues that are discussed/debated in the American mathematical community with a lot of excitement. (I did not really understand.) (Actually there was a thorough and nice discussion on Facebook a year ago about double-blind refereeing which seems a small corner of the large excitement.)

]]>**Speaker:** Gil Kalai, Hebrew University of Jerusalem, Reichman University and NYU

**Location:** Warren Weaver Hall 1302

**Date:** Monday, November 8, 2021, 3:45 p.m.

**Synopsis: **I will start with the analysis of Boolean functions and the related theory of noise stability and noise sensitivity. Next, I will discuss the sensitivity of noisy intermediate scale quantum (NISQ) computers, and explain why NISQ computers are computationally primitive and incapable of demonstrating neither “quantum computational advantage” nor the harder task of quantum error-correction. Finally, I will briefly discuss recent papers claiming a huge quantum computational advantage for NISQ systems which appears to be in sharp contrast with my theory.

Introductory video: click here.; Here is the presentation; Here is the colloquium page.

I plan to give a blackboard talk. The title is very similar to my ICM 2018 lecture except that a lot has happened since 2018.

- Helly-type problems with emphasis on the cascade conjecture
- Problems about convex polytopes (see this post)

My lecture in LUMS, was entitled “A word devoid of quantum computers with emphasis on predictability and free will”. Here is the presentation and here is the seminar page with links to the video recording (and to other interesting lectures). The lecture is related to this post on quantum computers and free will.

The last slide of the NYU introductory presentation. (I plan a blackboard lecture.)

At the end I gave a presentation. Here are the slides for the full representation. Apparently it was the first live Courant colloquium after almost two years.

Picture: Vlad Vicol

Picture: Deane Young

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