▁International ▁Committee ▁composed ▁to ▁organ ise ▁the ▁International ▁Congress es ▁for ▁the ▁Unity ▁of ▁Science . ▁ ▁He ▁died ▁in ▁ 1 9 5 1 ▁in ▁Paris ▁after ▁a ▁long ▁ill ness . ▁ ▁In ▁ 1 9 7 6 , ▁a ▁lun ar ▁cr ater ▁was ▁named ▁after ▁him . ▁Before , ▁it ▁was ▁designated ▁Ap oll on ius ▁D . ▁ ▁Work ▁In ▁the ▁Tra v aux , ▁Cart an ▁breaks ▁down ▁his ▁work ▁into ▁ 1 5 ▁areas . ▁Using ▁modern ▁termin ology , ▁they ▁are : ▁▁ ▁Lie ▁theory ▁ ▁Represent ations ▁of ▁Lie ▁groups ▁ ▁Hyper complex ▁numbers , ▁division ▁al gebras ▁ ▁Systems ▁of ▁P DE s , ▁Cart an – K äh ler ▁theorem ▁ ▁Theory ▁of ▁equivalence ▁ ▁In te gra ble ▁systems , ▁theory ▁of ▁prolong ation ▁and ▁systems ▁in ▁in volution ▁ ▁In finite - dimensional ▁groups ▁and ▁pseud og r oups ▁ ▁D iffer ential ▁geometry ▁and ▁moving ▁frames ▁ ▁General ised ▁spaces ▁with ▁structure ▁groups ▁and ▁connections , ▁Cart an ▁connection , ▁hol onomy , ▁W ey l ▁tensor ▁ ▁Ge ometry ▁and ▁topology ▁of ▁Lie ▁groups ▁ ▁Riemann ian ▁geometry ▁ ▁Sym metric ▁spaces ▁ ▁Top ology ▁of ▁compact ▁groups ▁and ▁their ▁hom ogeneous ▁spaces ▁ ▁Integr al ▁invari ants ▁and ▁classical ▁mechan ics ▁ ▁Rel ativity , ▁spin ors ▁ ▁Cart an ' s ▁mathematical ▁work ▁can ▁be ▁described ▁as ▁the ▁development ▁of ▁analysis ▁on ▁differenti able ▁manif olds , ▁which ▁many ▁now ▁consider ▁the ▁central ▁and ▁most ▁vital