Tobias Holck Colding (born 1963) is a Danish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working on geometric analysis, and low-dimensional topology. He is the great grandchild of Ludwig August Colding.

Biography

He was born in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Danish Realm, Kingdom of Denmark ...

, to Torben Holck Colding and Benedicte Holck Colding. He received his Ph.D. in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

in 1992 at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

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 New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

in various positions from 1992 to 2008. He has also been a visiting professor at MIT (2000–01) and at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

(2001–02) and a postdoctoral fellow at MSRI (1993–94). Colding lives in Cambridge, MA, with his wife and three children.

Work

In the early stage of his career, Colding did impressive work on

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

s with bounds on Ricci curvature. In 1995 he presented this work at the

Geometry Festival The Geometry Festival is an annual mathematics conference held in the United States. The festival has been held since 1985 at the University of Pennsylvania, the University of Maryland, Baltimore, University of Maryland, the University of North Ca ...

. He began working with

Jeff Cheeger Jeff Cheeger (born December 1, 1943, Brooklyn, New York City) 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 ...

while at NYU. He gave a 45-minute invited address to the ICM on this work in 1998 in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

. He began coauthoring with William P. Minicozzi at this time: first on

harmonic functions In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, : \f ...

, later on minimal surfaces, and now on

mean curvature flow In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surf ...

Recognition

He gave an

AMS AMS or Ams may refer to: Organizations Companies * Alenia Marconi Systems * American Management Systems * AMS (Advanced Music Systems) * ams AG, semiconductor manufacturer * AMS Pictures * Auxiliary Medical Services Educational institutions * A ...

Lecture at

University of Tennessee The University of Tennessee (officially The University of Tennessee, Knoxville; or UT Knoxville; UTK; or UT) is a public land-grant research university in Knoxville, Tennessee. Founded in 1794, two years before Tennessee became the 16th state, ...

. He also gave an invited address at the first AMS-Scandinavian International meeting in Odense,

, 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 , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

and gave the 2010 Cantrell Lectures at

University of Georgia , mottoeng = "To teach, to serve, and to inquire into the nature of things.""To serve" was later added to the motto without changing the seal; the Latin motto directly translates as "To teach and to inquire into the nature of things." , establ ...

. Since 2008 he has been a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

, and since 2006 a foreign member of the

Royal Danish Academy of Sciences and Letters {{Infobox organization , name = The Royal Danish Academy of Sciences and Letters , full_name = , native_name = Det Kongelige Danske Videnskabernes Selskab , native_name_lang = , logo = Royal ...

, and also since 2006 an honorary professor of

University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

. In 2010 Tobias H. Colding received the

Oswald Veblen Prize in Geometry __NOTOC__ 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. The Veblen Prize is now worth US$5000, and is ...

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'' (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."

Honors

Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

* ICM Speaker *

Carlsberg Foundation Carlsberg Foundation ( da, Carlsbergfondet) was founded by J. C. Jacobsen in 1876, by allocating some of his shares in the Carlsberg Brewery to fund and operate the Carlsberg Laboratory and the Museum of National History at Frederiksborg Palace. ...

Research Prize 2016

Major publications

* Cheeger, Jeff; Colding, Tobias H. ''Lower bounds on Ricci curvature and the almost rigidity of warped products.'' Ann. of Math. (2) 144 (1996), no. 1, 189–237. * Colding, Tobias H. ''Ricci curvature and volume convergence.'' Ann. of Math. (2) 145 (1997), no. 3, 477–501. * Cheeger, Jeff; Colding, Tobias H. ''On the structure of spaces with Ricci curvature bounded below. I.'' J. Differential Geom. 46 (1997), no. 3, 406–480. * Cheeger, Jeff; Colding, Tobias H. ''On the structure of spaces with Ricci curvature bounded below. II.'' J. Differential Geom. 54 (2000), no. 1, 13–35. * Cheeger, Jeff; Colding, Tobias H. ''On the structure of spaces with Ricci curvature bounded below. III.'' J. Differential Geom. 54 (2000), no. 1, 37–74. * Colding, Tobias H.; Minicozzi, William P., II. ''Generic mean curvature flow I: generic singularities.'' Ann. of Math. (2) 175 (2012), no. 2, 755–833.

References

External links

* {{DEFAULTSORT:Colding, Tobias Living people Differential geometers 21st-century Danish mathematicians University of Pennsylvania alumni Massachusetts Institute of Technology School of Science faculty Courant Institute of Mathematical Sciences faculty 20th-century Danish mathematicians 1963 births