Anne Duncan in 1968 on a 1960 paper by Robert Steinberg —
_______________________________________________________________________________
Related remarks in this journal — Steinberg + Chevalley.
Related illustrations in this journal — 4×4.
Related biographical remarks — Steinberg Deathdate.
From the American Mathematical Society (AMS) webpage today —
From the current AMS Notices —
Related material from a post of Aug. 6, 2014 —
(Here "five point sets" should be "five-point sets.")
From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens 54, 59-79 (1992):
“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”
The above symplectic structure* now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).
* The phrase as used here is a deliberate
abuse of language . For the real definition of
“symplectic structure,” see (for instance)
“Symplectic Geometry,” by Ana Cannas da Silva
(article written for Handbook of Differential
Geometry , Vol 2.) To establish that the above
figure is indeed symplectic , see the post
Zero System of July 31, 2014.
From Gotay and Isenberg, "The Symplectization of Science,"
Gazette des Mathématiciens 54, 59-79 (1992):
"… what is the origin of the unusual name 'symplectic'? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure 'line complex group' the 'symplectic group.'
… the adjective 'symplectic' means 'plaited together' or 'woven.'
This is wonderfully apt…."
The above symplectic structure** now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).
Some related passages from the literature:
* The title is a deliberate abuse of language .
For the real definition of "symplectic structure," see (for instance)
"Symplectic Geometry," by Ana Cannas da Silva (article written for
Handbook of Differential Geometry, vol 2.) To establish that the
above figure is indeed symplectic , see the post Zero System of
July 31, 2014.
** See Steven H. Cullinane, Inscapes III, 1986
Today is the birthday of mathematician Jean-Pierre Serre.
Some remarks related to today's day number within the month, "15"—
The Wikipedia article on finite geometry has the following link—
Carnahan, Scott (2007-10-27), "Small finite sets", Secret Blogging Seminar, http://sbseminar.wordpress.com/2007/10/27/small-finite-sets/, notes on a talk by Jean-Pierre Serre on canonical geometric properties of small finite sets.
From Carnahan's notes (October 27, 2007)—
Serre has been giving a series of lectures at Harvard for the last month, on finite groups in number theory. It started off with some ideas revolving around Chebotarev density, and recently moved into fusion (meaning conjugacy classes, not monoidal categories) and mod p representations. In between, he gave a neat self-contained talk about small finite groups, which really meant canonical structures on small finite sets.
He started by writing the numbers 2,3,4,5,6,7,8, indicating the sizes of the sets to be discussed, and then he tackled them in order.
Related material on finite geometry and the indicated small numbers may, with one apparent exception, be found at my own Notes on Finite Geometry.
The apparent exception is "5." See, however, the role played in finite geometry by this number (and by "15") as sketched by Robert Steinberg at Yale in 1967—
See also …
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