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, mathematical structure, structure, space, Mathematica ...

working on

geometric analysis Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of ...

, and

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, ...

. He is the great grandchild of

Ludwig August Colding Ludwig August Colding (13 July 1815 – 21 March 1888) was a Danish civil engineer and physicist who articulated the principle of conservation of energy contemporaneously with, and independently of, James Prescott Joule and Julius Robert von Maye ...

Biography

He was born in

Copenhagen Copenhagen ( ) is the capital and most populous city of Denmark, with a population of 1.4 million in the Urban area of Copenhagen, urban area. The city is situated on the islands of Zealand and Amager, separated from Malmö, Sweden, by the ...

Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...

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

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

in 1992 at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

under Chris Croke. Since 2005 Colding has been a professor of mathematics at

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

. He was on the faculty at the

Courant Institute The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

in various positions from 1992 to 2008. He has also been a visiting professor at

(2000–01) and at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

(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 differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure ...

. 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) is an American mathematician and Silver Professor at the Courant Institute of Mathematical Sciences of New York University. His main interest is differential geometry and its connections with topology and an ...

while at NYU. He gave a 45-minute invited address to the

ICM ICM may refer to: Organizations * Irish Church Missions, an Anglican mission * Institut du Cerveau, the Paris Brain Institute, a research center * Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw * Interna ...

on this work in 1998 in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

. 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\colon U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that ...

, later on

minimal surfaces In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

, 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 sur ...

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 ...

Lecture at

University of Tennessee The University of Tennessee, Knoxville (or The University of Tennessee; UT; UT Knoxville; or colloquially UTK or Tennessee) is a Public university, public Land-grant university, land-grant research university in Knoxville, Tennessee, United St ...

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

Odense Odense ( , , ) is the third largest city in Denmark (after Copenhagen and Aarhus) and the largest city on the island of Funen. As of 1 January 2025, the city proper had a population of 185,480 while Odense Municipality had a population of 210, ...

, 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 The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

and gave the 2010 Cantrell Lectures at

University of Georgia The University of Georgia (UGA or Georgia) is a Public university, public Land-grant university, land-grant research university with its main campus in Athens, Georgia, United States. Chartered in 1785, it is the oldest public university in th ...

. Since 2008 he has been a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) 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 other ...

, and since 2006 a foreign member of the

Royal Danish Academy of Sciences and Letters The Royal Danish Academy of Sciences and Letters ({{Langx, da, Det Kongelige Danske Videnskabernes Selskab or ''Videnskabernes Selskab'') is a Danish academy of science. The Royal Danish Academy was established on 13 November 1742, and was create ...

, and also since 2006 an honorary professor of

University of Copenhagen The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. ...

. 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 funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is n ...

together with

William Minicozzi II William Philip 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 o ...

for their work on

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

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."

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 () is a not-for-profit organization that 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 ...

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