William Minicozzi II
Encyclopedia
William Minicozzi II is an American
mathematician
. He was born in Bryn Mawr, Pennsylvania
, in 1967.
in 1990 and received his Ph.D.
from Stanford University
in 1994 under the direction of Richard Schoen
. After graduating he spent a year at the Courant Institute of New York University
as a visiting member where he began working with Tobias Colding
on harmonic functions on Riemannian manifold
s,
work he was later invited to present at the Geometry Festival
. In 1995, he went to the Johns Hopkins University
,
with a National Science Foundation postdoctoral fellowship. He won a Sloan Fellowship
in 1998.
Minicozzi was promoted the J. J. Sylvester Professor of Mathematics at Johns Hopkins in 2002 and is currently a Krieger-Eisenhower Professor in there. He turned to work on minimal surfaces, continuing to work with Tobias Colding
.
He gave an invited address on this work at the 2006 ICM
in Madrid, a London Mathematical Society Spitalfields Lecture in 2007, and will give the thirty-fifth University of Arkansas
Spring Lecture Series in 2010, and an AMS invited address in Syracuse
in 2010.
In 2010 William P. Minicozzi received the Oswald Veblen Prize in Geometry
together with Tobias Colding
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 surface
s. In a series of papers they have developed a structure theory for minimal surfaces with bounded genus
in 3-manifold
s, 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 conjecture."
In addition to his teaching and research duties, Minicozzi serves as an editor of the American Journal of Mathematics
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
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 Bryn Mawr, Pennsylvania
Pennsylvania
The Commonwealth of Pennsylvania is a U.S. state that is located in the Northeastern and Mid-Atlantic regions of the United States. The state borders Delaware and Maryland to the south, West Virginia to the southwest, Ohio to the west, New York and Ontario, Canada, to the north, and New Jersey to...
, in 1967.
Career
Minicozzi graduated from Princeton UniversityPrinceton 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....
in 1990 and received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
in 1994 under the direction of Richard Schoen
Richard Schoen
Richard Melvin Schoen is an American mathematician. Born in Fort Recovery, Ohio, he received his PhD in 1977 from Stanford University where he is currently the Anne T. and Robert M. Bass Professor of Humanities and Sciences...
. After graduating he spent a year 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...
as a visiting member where he began working with Tobias Colding
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...
on harmonic functions on Riemannian manifold
Riemannian manifold
In Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...
s,
work he was later invited to present 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...
. In 1995, he went to the Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
,
with a National Science Foundation postdoctoral fellowship. He won a Sloan Fellowship
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 is distinct from the Sloan Fellows in business....
in 1998.
Minicozzi was promoted the J. J. Sylvester Professor of Mathematics at Johns Hopkins in 2002 and is currently a Krieger-Eisenhower Professor in there. He turned to work on minimal surfaces, continuing to work with Tobias Colding
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 gave an invited address on this work at the 2006 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 ....
in Madrid, a London Mathematical Society Spitalfields Lecture in 2007, and will give the thirty-fifth University of Arkansas
University of Arkansas
The University of Arkansas is a public, co-educational, land-grant, space-grant, research university. It is classified by the Carnegie Foundation as a research university with very high research activity. It is the flagship campus of the University of Arkansas System and is located in...
Spring Lecture Series in 2010, and an AMS invited address in Syracuse
Syracuse
Syracuse, as a place name, may refer to:In Italy:* Syracuse, Sicily* the Province of SyracuseIn the United States:* Syracuse, New York* Syracuse, Indiana* Syracuse, Kansas* Syracuse, Missouri* Syracuse, Nebraska* Syracuse, Ohio* Syracuse, Utah...
in 2010.
In 2010 William P. Minicozzi 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 Tobias Colding
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...
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 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 a series of papers they have developed a structure theory for minimal surfaces with bounded genus
Genus (mathematics)
In mathematics, genus has a few different, but closely related, meanings:-Orientable surface:The genus of a connected, orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. It...
in 3-manifold
3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
s, 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 conjecture."
In addition to his teaching and research duties, Minicozzi serves as an editor of the American Journal of Mathematics
American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.- History :The American Journal of Mathematics is the oldest continuously-published mathematical journal in the United States, established in 1878 at the Johns Hopkins University...
.
Honors
- Sloan Fellow
- Speaker at the International Congress of MathematiciansInternational Congress of MathematiciansThe 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 ....
- Oswald Veblen Prize in GeometryOswald Veblen Prize in GeometryThe 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...