Tobias Colding
Encyclopedia
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 (2000–01) and at Princeton University
(2001–02) and a postdoctoral fellow at MSRI
(1993–94).
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. Minnicozzi 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 will give 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 surface
s. 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:
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.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was born in Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
, to Torben Holck Colding and Benedicte Holck Colding. He received his Ph.D. in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in 1992 at the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
under Chris Croke. Since 2005 Colding has been a professor of mathematics at MIT
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
. He was on the faculty at the Courant Institute of New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
in various positions from 1992 to 2008. He has also been a visiting professor at MIT (2000–01) and at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
(2001–02) and a postdoctoral fellow at MSRI
Mathematical Sciences Research Institute
The Mathematical Sciences Research Institute , founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions...
(1993–94).
In the early stage of his career, Colding did impressive work on manifolds with bounds on Ricci curvature
Ricci curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume element of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space...
. In 1995 he presented this work at the Geometry Festival
Geometry Festival
-1985 at Penn:* Marcel Berger* Pat Eberlein* Jost Eschenburg* Friedrich Hirzebruch* Blaine Lawson* Leon Simon* Scott Wolpert* Deane Yang-1986 at Maryland:* Uwe Abresch, Explicit constant mean curvature tori...
. He began working with Jeff Cheeger
Jeff Cheeger
Jeff Cheeger , is a mathematician. Cheeger is professor at the Courant Institute of Mathematical Sciences at New York University in New York City. His main interests are differential geometry and its applications to topology and analysis.-Biography:He graduated from Harvard University with a B.A....
while at NYU. He gave a 45-minute invited address to the ICM
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
on this work in 1998 in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
. He began coauthoring with William P. Minnicozzi at this time: first on harmonic functions and later on minimal surfaces.
He gave an AMS
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
Lecture at University of Tennessee
University of Tennessee
The University of Tennessee is a public land-grant university headquartered at Knoxville, Tennessee, United States...
. He also gave an invited address at the first AMS-Scandinavian International meeting in Odense
Odense
The city of Odense is the third largest city in Denmark.Odense City has a population of 167,615 and is the main city of the island of Funen...
, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. 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
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
and will give the 2010 Cantrell Lectures at University of Georgia
University of Georgia
The University of Georgia is a public research university located in Athens, Georgia, United States. Founded in 1785, it is the oldest and largest of the state's institutions of higher learning and is one of multiple schools to claim the title of the oldest public university in the United States...
. Since 2008 he has been a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
, and since 2006 a foreign member of the Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters is a Danish non-governmental science Academy, founded 13 November 1742 by permission of the King Christian VI, as a historical Collegium Antiquitatum...
, and also since 2006 an honorary professor of University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
.
In 2010 Tobias H. Colding received the Oswald Veblen Prize in Geometry
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
together with William Minicozzi II
William Minicozzi II
William Minicozzi II is an American mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967.-Career:Minicozzi graduated from Princeton University in 1990 and received his Ph.D. from Stanford University in 1994 under the direction of Richard Schoen...
for their work on minimal surface
Minimal surface
In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....
s. 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 (2) 160 (2004), 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. (2) 160 (2004), no. 1, 69-92.
- "The Space of Embedded Minimal Surfaces of Fixed Genus in a 3-manifold. III. Planar Domains". Ann. of Math. (2) 160 (2004), no. 1, 523-572.
- "The Space of Embedded Minimal Surfaces of Fixed Genus in a 3-manifold. IV. Locally Simply Connected". Ann. of Math. (2) 160 (2004), no. 1, 573-615.
- "The Calabi-Yau Conjectures for Embedded Surfaces", Ann. of Math. (2) 167 (2008), 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.