Ramsey numbers, polar spaces, and oddtowns

I have uploaded a preprint which concludes a joint work with John Bamberg and Ferdinand Ihringer that started last year during their visit to TU Delft. In this work, we have done one of my favorite things in mathematics research: combining unrelated topics to create something new in each of them. Here is a quick […]

Ramsey numbers, polar spaces, and oddtowns

Love in Projective Planes, Chinese Valentine’s Day & Phonotactics
A part of the video.

A few days ago China celebrated one of many Chinese Valentine’s days: the 20th of May. Why is this a special day in China? Chinese has around 30 to 36 phonemes which is plenty, but Chinese phonotactics dictate that you can only make around 1200 syllables out of them, for instance, see this video. English has more than 8000 possible syllables. Additionally, Chinese (unlike many other languages) uses one syllables per morpheme. This distinguished from languages such as Japanese which have very few syllables, but usually use two or three syllables for one morpheme. Often Chinese avoids any resulting confusion by various means, for instance, by combining at least two morphemes/syllables. Yet you find around 1500 one syllable words in Mandarin. By the pigeonhole principle, we find at least two words which sound the same!

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Students and Robots

Last year Zhirayr Avetisyan and I created a math riddle about the games cops and robbers. It was part of an outreach event to high-school student at Ghent University. You can find it in this post here. The story was that a group of mathematicians wants to walk around the city of Ghent and have fun, while a group of bureaucrats wants to destroy that fun.

1. The New Version for SUSTech

This year I was asked to make a riddle for Pi Day at my new university, the Southern University of Science and Technology (SUSTech) in Shenzhen, China. Now I was asked very short notice, so I simply wanted to re-use last year’s riddle. There were two problems: (1) I can hardly use a city map of Ghent for a riddle at a university in Shenzhen. (2) In Belgium or Germany most civil servants and bureaucrats do not mind when people make fun of them. Indeed, I probably know all my civil servant jokes from civil servants (E.g.: Two civil servants meet in the hallway. One speak: “Oh! You cannot sleep either?”). Even though China is probably the most bureaucratic country which I have ever lived in (and I have lived in Germany, obviously), this is serious business and the story had to be replaced. The responsible secretary come up with a very cute story: A robot escaped from the robotics lab and students have to catch it again.

Here is the map of SUSTech’s campus:

map_sustech

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Refereeing

The work of mathematicians goes through peer-review which contributes to the acceptance of the correctness of our work. Peer-reviewers are of course peers, that is other mathematicians, and most of us consider this work important.

At least two of my colleagues complain about how much they have to referee and (they claim) give my name as an alternative peer-reviewer (instead of doing it themselves). As it is the end of the year, here the number of referee requests which I accepted in my life by year of acceptance. Note that 2015 might include 2013 and 2014. I know that many colleagues review far more papers than I do, but for certain not all of them and, hence, I hope that the chart below discourages some of my colleagues from recommending me as an alternative referee.

[This year I was not even a good referee as I lost track of some of my commitments which I agreed to during my move to China.]

Classifying Cameron-Liebler Sets/Boolean Degree 1 Functions

This week I put two new preprint on the arXiv. Both are on a similar theme, so I will discuss them together. One is with Morgan Rodgers on regular sets of lines in rank 3 polar spaces. The other one is solves a problem which I have been thinking about very regularly since November 2017: The classification of Boolean degree {1} functions (or Cameron-Liebler classes) of {k}-spaces in an {n}-dimensional vector space {V} over the field with {q} elements for {n} large enough (and {q} and {k \geq 2} fixed).

Not only did I (and many other researcher) try to solve this problem for many years, it also turns out that the solution has a very short and concise proof. So for now I am very happy about it. [And please do not find a mistake. Any mistake must be embarrissingly simple.] The problem itself (for {k=2}) goes back to a paper by Cameron and Liebler in 1982, so it is also a reasonably old problem.

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Post-Doc Positions at SUSTech, Shenzhen

This is not a proper “I have jobs! Please apply!” post, but more a general service announcement. It is my understanding that I can essentially have up to two post-docs here at the Southern University of Science and Technology (SUSTech) in Shenzhen without having to worry about funding too much. Shenzhen is one of the most prosperous cities of China. It is located next to Hong Kong, maybe 20 minutes by high-speed rail Well-known companies such as Huawei, Tencent, and BYD are based in Shenzhen. The mathematics department has a strong combinatorics and algebra group, including (in no particular ordering) Qing Xiang, Ziqing Xiang, Caiheng Li, Efim Zelmanov, and Vyacheslav Futorny.

There is some process and formal application process involved which I do not yet understand too much, but I assume that it is not difficult. I had postdoc positions in Belgium, Canada, Germany, and Israel. The salary of a postdoc in Shenzhen is comparable to these. I also talked to several current and former postdocs at SUSTech. They all seem to be happy with their working conditions.

Now why am I writing this? If anyone considers doing a postdoc with me, then write me an e-mail and I can figure out details. So this post tells you about this option. Of course you should work in an area which is sufficiently close to my research. Anything in finite geometry, algebraic combinatorics, or those parts of coding theory and extremal combinatorics which I like are good.

I also seem to have 0.5 PhD positions per year. My current impression is that it is probably not advisable for non-Chinese and that the salaries are not competitive with those in Belgium, Canada or Germany (my current points of reference, see above). Everyone is also very welcome to ask me about that.

Interlacing and the Second Largest Eigenvalue

Apparently, I described a very elegant argument to give a lower bound on the second largest eigenvalue of the adjacency matrix of a regular graph last year. This was pointed out in two recent preprints by Eero Räty, Benny Sudakov, and Istvan Tomon. This blog post is to describe the very short argument and how I derived it (stole it) from a remark in the book Distance-Regular Graphs by Brouwer, Cohen, and Neumaier (BCN). This shows yet again that BCN is an endless source of wisdom if you find the right interpretation of the words written there.

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Move to China & Blog Picture & Data Storage

Let me start with a small service announcement. In November I am taking up a position as an tenure-track assistant at the Southern University of Science and Technology in Shenzhen. At least if everything goes well. Airplanes can crash or I could fail the medical examination. The date of my flight is easy to remember. So here is that. People no longer have to ask me.

Then I recently figured out how to make polls, so let me do another one. I started this blog in 2017 when I was a postdoc of Gil Kalai in Jerusalem. Just a few days prior to my first post I visited the Mount of Olives with my housemate Agata, her husband, and my girlfriend/partner at the time. A picture from there became the banner picture of this blog. Now I moved from Israel to Belgium around January/February 2018, so maybe I should change it at some point. But to what? Something in Shenzhen? They have fancy buildings there (just not that old as the city is from 1979, slightly younger than Jerusalem):

But maybe something math-related would be more appropriate. This would require some thinking on my part. Surely, feasible. In any case, here is a poll. I will not implement any change soon (it took me months to write this post).

My next post, whenever that will be, is again about some math. Or maybe about moving my strongly regular graph data to a better place. People tell me that Zenodo might be good option. It even gives your data a DOI and, probably, CERN will exist for quite some time. Let’s see …