▁of ▁Dar b oux ▁and ▁T ann ery , ▁and ▁met ▁Cart an ▁for ▁the ▁first ▁time . ▁ ▁Cart an ▁def ended ▁his ▁dis sert ation , ▁The ▁structure ▁of ▁finite ▁continuous ▁groups ▁of ▁transformations ▁in ▁ 1 8 9 4 ▁in ▁the ▁Fac ulty ▁of ▁Sciences ▁in ▁the ▁Sor bon ne . ▁Between ▁ 1 8 9 4 ▁and ▁ 1 8 9 6 ▁Cart an ▁was ▁a ▁lect urer ▁at ▁the ▁University ▁of ▁Mont pel lier ; ▁during ▁the ▁years ▁ 1 8 9 6 ▁through ▁ 1 9 0 3 , ▁he ▁was ▁a ▁lect urer ▁in ▁the ▁Fac ulty ▁of ▁Sciences ▁at ▁the ▁University ▁of ▁Lyon . ▁ ▁In ▁ 1 9 0 3 , ▁while ▁in ▁Ly ons , ▁Cart an ▁married ▁Marie - Lou ise ▁Bian con i ▁( 1 8 8 0 – 1 9 5 0 ); ▁at ▁the ▁same ▁year , ▁Cart an ▁became ▁a ▁professor ▁in ▁the ▁Fac ulty ▁of ▁Sciences ▁at ▁the ▁University ▁of ▁Nancy . ▁In ▁ 1 9 0 4 , ▁Cart an ' s ▁first ▁son , ▁Henri ▁Cart an , ▁who ▁later ▁became ▁an ▁influ ential ▁math ematic ian , ▁was ▁born ; ▁in ▁ 1 9 0 6 , ▁another ▁son , ▁Jean ▁Cart an , ▁who ▁became ▁a ▁composer , ▁was ▁born . ▁In ▁ 1 9 0 9 ▁Cart an ▁moved ▁his ▁family ▁to ▁Paris ▁and ▁worked ▁as ▁a ▁lect urer ▁in ▁the ▁Fac ulty ▁of ▁Sciences ▁in ▁the ▁Sor bon ne . ▁In