The (Random) Matrix and more

Three pictures, and a few related links.

Van Vu

Spoiler: In one of the most intense scenes, the protagonist, with his bare hands and against all odds, took care of the mighty Wigner semi-circle law in two different ways. (From VV’s FB)

More information on Van Vu’s series of lectures. Van Vu’s home page; Related posts: did physicists really just prove that the universe is not a computer simulation—that we can’t be living in the Matrix? (Shtetl-Optimized); A related 2012 post on What’s New;

Two more pictures the first also from FB

Saharon Shelah

Shaharon Shelah ICM 1974 (Vancouver) (Mohammad Golshani over FB)

See my post A theorem about infinite cardinals everybody should know; Gowers’s post Two infinities that are surprisingly equal about a recent breakthrough result by Maryanthe Malliaris and Saharon Shelah; and a recent 4-page solution to a conjecture of Spencer on finitary Hindman numbers by Shahram Mohsenipour and Shelah.  More information on the last paper: (1) It is an Iranian-Israeli collaboration (2) Spencer asked Shelah the question during the workshop: Combinatorics: Challenges and Applications, celebrating Noga Alon’s 60th birthday, Tel Aviv University, January 17-21, 2016. (3) This is paper 1146 in Shelah’s (main) list of publications. Shelah’s 1974 lecture was called “Why There Are Many Nonisomorphic Models for Unsuperstable Theories.”

Sándor Szalai,  Catherine Rényi, Alfréd Rényi András Hajnal and Paul Erdős

From left: Sándor Szalai,  Catherine Rényi, Alfréd Rényi, András Hajnal and Paul Erdős (Matrahaza ) The picture is from Janos Pach’s Lancaster lecture, who also discussed how Szalai came up with Ramsey’s theorem. (See also Noga Alon and Michel Krivelevich’s chapter Extremal and Probabilistic Combinatorics, In: Princeton Companion to Mathematics, W. T. Gowers, Ed., Princeton University Press 2008, pp. 562-575.)

In the course of an examination of friendship between children some fifty years ago, the Hungarian sociologist Sandor Szalai observed that among any group of about twenty children he checked he could always find four children any two of whom were friends, or else four children no two of whom were friends. Despite the temptation to try to draw sociological conclusions, Szalai realized that this might well be a mathematical phenomenon rather than sociological one.  He got interested in the problem, discussed it with  Erdős, Rényi , and Turán and in a short time he came up with a number of interesting constructions. In fact, he obtained record lower bound estimates for several Ramsey numbers.

(Janos’ further remarks: “Sandor (Alexander) Szalai was a well known Hungarian sociologist and a famously bright and witty man. I am not sure whether he was the first to notice and study the the laws of clique- and anti-clique formation among groups of schoolchildren, but I suspect that he was not. The sociology of small groups used to be a popular alternative to more “dangerous” Marxist theories of classes in the 50-ies and 60-ies. My guess would be that Szalai discussed these issues and was fascinated by this subject some time around 1960. It is fair to say that he independently conjectured Ramsey’s theorem.”)