Re: Gelfand, NCG

[Iga Nguyen <iga@blue.cft.edu.pl>]

Hello,

On Mon, 18 Oct 1999, Phung Ho Hai wrote:

> Ca'c nha va^.t ly' invented tensor product song ra^'t nhie^`u nguo+.i
> la`m va^.t ly' ly' thuye^'t kho^ng hie^?u duo.c kha'i nie^.n tensor
> product trong toa'n ho.c.

DDi.nh nghi~a tru+`u tu+o+.ng nhu+ tensor product nhu+ va^.y thi` ma^'y
ng` hie^?u :-))  Co' hie^?u thi` cu~ng cha(?ng nhi`n tha^'y ca'i gi`
ngoa`i ma^'y ca'i cu.c ga.ch su+'t me? va` ma^'y ca'i mu~i te^n :-))
  Tru+`u tu+o+.ng hoa' nhu+~ng thu+' co' the^? so+` mo' ddu+o+.c
cu~ng to^'t, ddo' la` 1 style, nhu+ng ra^'t i't ng` co' kha? na(ng 
"so+` mo'" la.i nhu+~ng thu+' dda~ "ddu+o+.c" tru+`u tu+o+.ng ho'a o+? 
mu+'c cao va` ke^'t cu.c la` xua^'t hie^.n ... 1 dda`n bo`.
  Anh Ha?i no'i ddu'ng, ho. kho^ng hie^?u tha^.t nhu+ng kho^ng pha?i
vi` ho. kho^ng co' kha? na(ng hie^?u, ma` va^'n dde^` la` o+? cho^~
what for ?, i.e. ho. ra^'t co' y' thu+'c la` ho. kho^ng ca^`n dde^'n no'.
As a matter of fact, 99% people la`m VLLT chi? coi Math nhu+ la` co^ng
cu. cu?a ho. trong co^ng vie^.c, cu`ng la('m thi` coi Math la` their
language ne^n cu~ng kho^ng the^? ddo`i ho?i nhie^`u.  Cu~ng tu+o+ng tu+. 
95% computer's users kho^ng hie^?u the concept of theoretical computer,
operating systems, protocols, tha^.m tri' demons, data bases, etc. nhu+ng 
no' co' a?nh hu+o+?ng gi` dde^'n hie^.u qua? co^ng vie^.c cu?a ho. 
dda^u ? :-) Ai cu~ng sa`i telephone, TV, CD ha`ng nga`y, nhi`n tha^'y
ddu? loa.i kie^'n tru'c ky` qua(.c, nhu+ng ma^'y ai hie^?u dde^'n no+i
dde^'n tro^'n ve^` no' dda^u :-)  
  
> A` anh co`n ba('t be? hai ca'i thua^.t ngu+~ topo va` geometry. Topo la`
> gi` ne^'u nhu+ kho^ng pha?i la` hi`nh ho.c. Nghie^n cu+'u hi`nh ho.c trong
> toa'n kho^ng nha^'t thie^'t la` cu+' pha?i co' mo^.t toa'n tu+? De Rham.
> Thua^.t ngu+~ geometry anh hie^?u trong toa'n go.i la` mo^.t differential
> structure.

O+? MGU co' department, namely "Geometry & Topology" cha('c o+? ddo' 
ho. tuye^n truye^`n nhu+ dza^.y ha? :-)  Topo ro^.ng ho+n hi`nh ho.c
nhie^`u chu+' Ha?i, eg. trong Set Topology thi` to^i chu+a nhi`n tha^'y
ca'i co' the^? go.i la` hi`nh ho.c ddu+o+.c :-) 
 Tho+`i xu+a co' 1 mathematician namely Schouten (famous "geometer"
before WW2) ddo^'i vo+'i o^?ng ta thi` hi`nh ho.c la` toa`n ca'c ky'
hie^.u ca^y tho^ng ddo^.i mu~ co^'i ro^`i treo dde`n lu?ng la(?ng be^n 
tra'i be^n pha?i tre^n du+o+'i (its indexes).  /O^?ng ta cu~ng dde^? la.i
kho^'i thu+' hay ho cho ha^.u the^'/ :-)
  Co`n anh AV thi` a?nh a^'y ra^'t ye^u smooth manifolds ne^n
chi? co' differential geometry a?nh a^'y hie^?u la` Geometry :-)  
A?nh a^'y cu~ng kho^ng co^ng nha^.n algebraic geometry hay discrete
geometry la` hi`nh ho.c :-))
  
> Ca'i triple ma` anh no'i de^'n co' the^? hie^?u la` "mo^.t kg topo
> (non-comm), mo^.t diff. structure va` mo^.t phe'p ti'ch pha^n"
> Ca'i da.i so^' A trong ca'i triple a^'y no' pha^n ba^.c va` tha`nh pha^`n
> ba^.c 0 xa'c di.nh kg. topo (non-comm)-bo+?i do^'i nga^~u Gelfand.

Gho+'m gi` ma` ra('c ro^'i the^'.   Cu+' no'i qua'ch la` ca'i kho^ng 
gian ddo^'i nga^~u nhu+ va^.y cha(?ng qua la` object in the oposite
category of the non-commutative algebras (C^*-algebras) la` xong :-) 

Cheers,
Iga