More Annotated Pictures from Fall/Winter 2024

• Pictures from Jerusalem, Tel Aviv, and Athens (!) and Rehovot.
• The new Google‘s 10,000,000,000,000,00,000,000,000,000 supremacy announcement; 
• Sarnak’s lectures; the “A-Bass note”  and, fullerences, 3-polytopes with hexagonal and pentagonal faces (answer to TYI58);
• What was the music in the ancient Jewish Temple?
• Winter school in Rehovot; Terrific quantum error-correcting codes; 
  
• A picture with my grandchildren and more.

December 2024

Jerusalem: Einstein Institute of Mathematics

With Itamar Zwick and Shahar Mozes and Yuka.

Tel Aviv Museum and skyline

Nava de-Shalit, Udi de-Shalit, Mazi and I on the rooftop of the Tel Aviv Museum.

Google‘s 10,000,000,000,000,000,000,000,000 supremacy announcement

The Google willow announcement. (Left:) Sundar Pichai’s tweet and Elon Musk’s reply. (Right:) The announcement boosted stock values for quantum computing companies (but had no effect on Bitcoin’s price). Google’s claim of exponential increase in reducing-error capabilities is based on alleged exponential growth of the function: Λ(5)=1; Λ(7)=2 .

Here are some remarks on the latest sensational supremacy claim. Just a few hours before the announcement, I explained—based on Google‘s 2019 claims— why the scientific claims made by Google Quantum AI should not be taken too seriously. 

Until this latest announcement, I mistakenly believed (and hoped) that after the 2019 supremacy claim, the Google Quantum AI team had largely shifted toward more fruitful directions. However, the new “septillion” claim retrospectively justifies our efforts over the past five years to meticulously scrutinize Google’s 2019 supremacy experiment.

Beyond serious concerns regarding Google’s methodology, these new extraordinary supremacy claims also appear to conflict with results on classical spoofing by Gao et al. and by Aharonov et al.

Does an assertion by Sundar Pichai, followed by a “wow” from Elon Musk, now constitute a new scientific proof system? We have already seen trillion-dollar companies and multi-billionaires (arguably) reshape democracy—should we now expect them to redefine the nature of science as well?  

The Cascade Lectures in Combinatorics

Tricia Hersh invited me to give one of the Cascade Lectures in Combinatorics (CALICO). What could be more appropriate than to talk about: The Cascade Conjecture, Topology, and the Four-Color Theorem. (Slides: cascade; video.)

Athens!

For the first time since the beginning of the terrible war we went to a few days trip abroad, to wonderful Athens.

For a mathematician, seeing all these Greek letters coming alive is an interesting experience!

Sarnak’s lectures and workshop

Peter Sarnak

Fullerences

Peter Sarnak talked about the remarkable class of simple three-dimensional polytopes with (only) pentagonal and hexagonal faces. Let F be the class of planer 3-connected cubic graphs with n vertices so that all faces (including the outer face) are 5-gons or 6-gons. (Equivalently, F can be regarded as graphs of simple 3-polytopes with 5-sided and 6-sided faces.) Such polytopes arouse in chemistry and they are called Fullerenes. It follows from Euler’s theorem that among the 2-faces there are always 12 pentagons. We asked in the previous post

Test your intuition (58): Does the number of graphs in F with n vertices grows exponentially or polynomially with the number of vertices?

Answer to test your intuition (58): The number is roughly . It is polynomial in .

Peter mentioned remarkable papers by Thurston, Shapes of polyhedra and triangulations of the sphere (1998), and by Engel, Goedgebeur, and Smillie, Exact enumeration of fullerenes (2023).  I am not aware of a direct combinatorial argument for the polynomial growth rate. (ChatGPT’s answer was: exponential.)

Now, what about higher dimensions?

What is the origin of the term “The A-Bass note”?

I asked Peter if the term is related to the famous mathematician Hyman Bass. But, no, it is related to the bass note in music and refers to the lowest eigenvalues. 

New members lectures at the Israeli Academy of Sciences and Humanities 

Lectures by 4 of the new members of the Israeli Academy of Science and humanities.  Top left Miki Elad, top right Ashraf Brik, bottom left: Tamar Dayan and bottom right: Edwin Seroussi. I always liked these short lectures aimed for a large audience. 

Edwin Seroussi is an Israeli musicologist.  He is often being asked, “Professor, what was the music in the Jewish Temple?” His fascinating lecture was devoted to answers to this question. A prominent role in the talk played Shabbethai Meshorer Bass (1641–1718) a Jewish scholar born in Kalitz in 1641, who moved to Prague at the age of 14 after both his parents died in persecutions during the Russo-Swedish war. Bass was a bass singer in the Altneuschule synagogue of Prague and his name was derived from his position. 

You may wonder if Hyman Bass is related to Shabbethai Bass, but as Hyman (Chaim) told me the answer is:  “No, My parents were both from Lithuania. ‘Bass’ was the Ellis Island (immigration) translation of Bashekevich. At least one fourth generation descendent has reinstalled that name.”

Winter school on expansion in groups, combinatorics, and complexity

Speakers of the first day: Gil Cohen, Nir Lazarovich, Amir Yehudayoff, Esty Kelman, and Pavel Panteleev.

Outstanding quantum error-correcting codes

Pavel Panteleev gave a beautiful lecture on classical and quantum low-density parity-check (LDPC) codes, classical good locally testable (LTC) codes, and the quest for good quantum locally testable codes. (Here, “good” is not just a compliment—it refers to codes with positive rate.) The recent paper Maximally Extendable Product Codes are Good Coboundary Expanders by Gleb Kalachev and Pavel Panteleev brings us closer to this goal, with high-dimensional expanders (HDX) playing a crucial role. 

We previously discussed some earlier breakthroughs here and here. (And Quanta Magazine covered them here and here.) Here is a post about a 2014 workshop on Quantum PCP and/or Quantum Codes and HDX.

Gleb and Pavel are also leading contributors to classical spoofing algorithms for random circuit sampling. Their algorithms enabled the confirmation of certain fidelity estimates for large circuits in Google‘s 2019 quantum supremacy paper. Over the past few years, Yosi Rinott, Tomer Shoham and I have had several fruitful collaboration with them on this topic, and they were very helpful to our project. 

More pictures

With my grandchildren Yonatan, Yoav, and Ilan

With Boris Solomyak (left), Moshe White and Dror Bar-Nathan (right). Dror told me about his 2022 paper with  Roland van der Veen on exciting efficiently-computable knot invariants.  Stay tuned!

Dror also found three pictures from the late eighties. Yuval Peres, Dror, Shahar Mozes, and me. (The right picture from Princeton and the other two from Yale.) 

Tel Aviv beach