Tobias Colding

Last updated
Tobias Colding
Born1963 (age 5960)
Nationality Danish
Alma mater University of Pennsylvania
Awards Veblen Prize in Geometry (2010)
Scientific career
Fields Mathematics
Institutions Massachusetts Institute of Technology
New York University
Doctoral advisor Christopher Croke

Tobias Holck Colding (born 1963) is a Danish mathematician working on geometric analysis, and low-dimensional topology. He is the great grandchild of Ludwig August Colding.



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). Colding lives in Cambridge, MA, with his wife and three children.


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. [1] He began coauthoring with William P. Minicozzi at this time: first on harmonic functions, later on minimal surfaces, and now on mean curvature flow.


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. [2] 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." [3]


Major publications

Related Research Articles

In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.

<span class="mw-page-title-main">Riemannian geometry</span> Branch of differential geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.

<span class="mw-page-title-main">Grigori Perelman</span> Russian mathematician (born 1966)

Grigori Yakovlevich Perelman is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. He is widely regarded as one of the greatest living mathematicians.

<span class="mw-page-title-main">Shing-Tung Yau</span> Chinese mathematician

Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University.

<span class="mw-page-title-main">Richard S. Hamilton</span> American mathematician

Richard Streit Hamilton is an American mathematician who serves as the Davies Professor of Mathematics at Columbia University. He is known for contributions to geometric analysis and partial differential equations. Hamilton is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. However, Perelman declined the award, regarding Hamilton's contribution as being equal to his own.

<span class="mw-page-title-main">Mikhael Gromov (mathematician)</span> Russian-French mathematician

Mikhael Leonidovich Gromov is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of IHÉS in France and a professor of mathematics at New York University.

<span class="mw-page-title-main">Simon Donaldson</span> English mathematician

Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.

<span class="mw-page-title-main">Richard Schoen</span> American mathematician

Richard Melvin Schoen is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984.

<span class="mw-page-title-main">Tian Gang</span> Chinese mathematician (born 1958)

Tian Gang is a Chinese mathematician. He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University. He is known for contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis.

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 awarded every three years.

<span class="mw-page-title-main">Jeff Cheeger</span> American mathematician

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 connections with topology and analysis.

The Geometry Festival is an annual mathematics conference held in the United States.

<span class="mw-page-title-main">Leon Simon</span> Australian mathematician (born 1945)

Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.

William Philip Minicozzi II is an American mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967.

Guofang Wei is a mathematician in the field of differential geometry. She is a professor at the University of California, Santa Barbara.

<span class="mw-page-title-main">Gerhard Huisken</span> German mathematician

Gerhard Huisken is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him. With Tom Ilmanen, he proved a version of the Riemannian Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity.

In mathematics, the Almgren–Pitts min-max theory is an analogue of Morse theory for hypersurfaces.

Xiuxiong Chen is a Chinese-American mathematician whose research concerns differential geometry and differential equations. A professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen Prize in Geometry in 2019. In 2019, he was awarded the Simons Investigator award.

<span class="mw-page-title-main">Sylvestre Gallot</span> French mathematician

Sylvestre F. L. Gallot is a French mathematician, specializing in differential geometry. He is an emeritus professor at the Institut Fourier of the Université Grenoble Alpes, in the Geometry and Topology section.

In the mathematical field of differential geometry, the Simons formula is a fundamental equation in the study of minimal submanifolds. It was discovered by James Simons in 1968. It can be viewed as a formula for the Laplacian of the second fundamental form of a Riemannian submanifold. It is often quoted and used in the less precise form of a formula or inequality for the Laplacian of the length of the second fundamental form.


  1. Colding, Tobias H. (1998). "Spaces with Ricci curvature bounds". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 299–308.
  2. "Colding, Seidel win 2010 AMS Veblen Prize in Geometry".
  3. American Mathematical Society, January 2010 Prizes and Awards, 2010 Joint Mathematics Meeting, San Francisco, CA, January 13–16, 2010.
  4. "404 | Carlsbergfondet".{{cite web}}: Cite uses generic title (help)