doctoral_advisor nationality fields workplaces article_title name alma_mater
christopher croke den danish mathematics new york university tobias colding
 tobias colding university of pennsylvania
tobias colding

tobias holck colding is a danish mathematician .
he was born in copenhagen , denmark , to torben holck colding and benedicte holck colding .
he received his ph.d. in mathematics in 1992 at the university of pennsylvania under chris croke .
since 2005 colding has been a professor of mathematics at mit .
he was on the faculty at the courant institute of new york university in various positions from 1992 to 2008 .
he has also been a visiting professor at mit -lrb- 2000 -- 01 -rrb- and at princeton university -lrb- 2001 -- 02 -rrb- and a postdoctoral fellow at msri -lrb- 1993 -- 94 -rrb- .
in the early stage of his career , colding did impressive work on manifolds with bounds on ricci curvature .
in 1995 he presented this work at the geometry festival .
he began working with jeff cheeger while at nyu .
he gave a 45-minute invited address to the icm on this work in 1998 in berlin .
he began coauthoring with william p. minicozzi at this time : first on harmonic functions and later on minimal surfaces .
he gave an ams lecture at university of tennessee .
he also gave an invited address at the first ams-scandinavian international meeting in odense , denmark , in 2000 and an invited address at the germany mathematics meeting in 2003 in rostock .
he gave the 2008 mordell lecture at the university of cambridge and gave the 2010 cantrell lectures at university of georgia .
since 2008 he has been a fellow of the american academy of arts and sciences , and since 2006 a foreign member of the royal danish academy of sciences and letters , and also since 2006 an honorary professor of university of copenhagen , denmark .
in 2010 tobias h. colding received the oswald veblen prize in geometry together with william minicozzi ii for their work on minimal surfaces .
in justification of the reward the american mathematical society wrote : `` the 2010 veblen prize in geometry is awarded to tobias h. colding and william p. minicozzi ii for their profound work on minimal surfaces .
in a series of papers they have developed a structure theory for minimal surfaces with bounded genus in 3-manifolds , which yields a remarkable global picture for an arbitrary minimal surface of bounded genus .
this contribution led to the resolution of long-standing conjectures of initiated a wave of new results .
specifically , they are cited for the following joint papers , of which the first four form a series of establishing the structure theory for embedded surfaces in 3-manifolds : `` the space of embedded minimal surfaces of fixed genus in a 3-manifold .
i. estimates off the axis for disks '' , `` ann .
of math '' -lrb- 2 -rrb- 160 -lrb- 2004 -rrb- , no. 1 , 27-68 .
`` the space of embedded minimal surfaces of fixed genus in a 3-manifold .
ii .
multi-valued graphs in disks '' .
`` ann .
of math . ''
-lrb- 2 -rrb- 160 -lrb- 2004 -rrb- , no. 1 , 69-92 .
`` the space of embedded minimal surfaces of fixed genus in a 3-manifold .
iii .
planar domains '' .
`` ann .
of math . ''
-lrb- 2 -rrb- 160 -lrb- 2004 -rrb- , no. 1 , 523-572 .
`` the space of embedded minimal surfaces of fixed genus in a 3-manifold .
iv .
locally simply connected '' .
`` ann .
of math . ''
-lrb- 2 -rrb- 160 -lrb- 2004 -rrb- , no. 1 , 573-615 .
`` the calabi-yau conjectures for embedded surfaces '' , `` ann .
of math . ''
-lrb- 2 -rrb- 167 -lrb- 2008 -rrb- , no. 1 , 211-243 .
in the final paper cited here , the authors show that a complete embedded minimal surface of finite genus is properly embedded , proving the embedded version of the calabi-yau conjectures . ''
tobias colding is the great grandchild of ludwig august colding .
