What key details about georges de rham can be extracted from the following bio? Bio: georges de rham -lrb- ; 10 september 1903 -- 9 october 1990 -rrb- was a swiss mathematician , known for his contributions to differential topology . he studied at the university of lausanne and then in paris for a doctorate , becoming a lecturer in lausanne in 1931 ; where he held positions until retirement in 1971 ; he held positions in geneva in parallel . in 1931 he proved de rham 's theorem , identifying the de rham cohomology groups as topological invariants . this proof can be considered as sought-after , since the result was implicit in the points of view of henri poincare and Elie cartan . the first proof of the general stokes ' theorem , for example , is attributed to poincare , in 1899 . at the time there was no cohomology theory , one could reasonably say : for manifolds the homology theory was known to be self-dual with the switch of dimension to codimension -lrb- that is , from h '' k '' to h '' n-k '' , where '' n '' is the dimension -rrb- . that is true , anyway , for orientable manifolds , an orientation being in differential form terms an '' n '' - form that is never zero -lrb- and two being equivalent if related by a positive scalar field -rrb- . the duality can be reformulated , to great advantage , in terms of the hodge dual -- intuitively , ' divide into ' an orientation form -- as it was in the years succeeding the theorem . separating out the homological and differential form sides allowed the coexistence of ' integrand ' and ' domains of integration ' , as '' cochains '' and '' chains '' , with clarity . de rham himself developed a theory of homological currents , that showed how this fitted with the generalised function concept . the influence of de rham 's theorem was particularly great during the development of hodge theory and sheaf theory . de rham also worked on the torsion invariants of smooth manifolds .
The answer to this question is:
- doctoral students is pierre jeanquartier serge maumary pierre-denis methee manoutcher vassal- known for is de curve rham 's theorem de rham cohomology de rham- fields is mathematics- death date is 09 october 1990- workplaces is university of lausanne university of geneva- doctoral advisor is henri lebesgue- awards is marcel benoist prize -lrb- 1965 -rrb-- birth date is 10 september 1903- name is georges de rham- nationality is swiss- death place is lausanne- birth place is roche , vaud- alma mater is university of paris university of lausanne