Fernando Codá Marques and André Neves to receive the 2016 AMS Oswald Veblen Prize

November 20, 2015

Fernando Codá Marques (Princeton University) and André Neves (Imperial College London) will receive the 2016 AMS Oswald Veblen Prize in Geometry for "their remarkable work on variational problems in differential geometry [including] the proof of the Willmore conjecture." The prize citation points in particular to a paper by Codá Marques and Neves, "Min-max theory and the Willmore conjecture," Annals of Mathematics (2014).

This work resolved a longstanding question about the nature of surfaces. The Willmore energy, sometimes called the bending energy, is a formula that describes how surfaces bend in different directions. For example, for a sphere, the Willmore energy is zero, because a sphere bends in exactly the same way at every point. The concept is named after mathematician Thomas J. Willmore (1919-2005), although it was known already in the early 19th century, when it was used for theoretical modeling of elastic shells.

Willmore knew that the sphere minimizes the Willmore energy. In 1965, he began thinking about how the Willmore energy behaves on other surfaces, in particular, on a torus, which is the mathematical name for the surface of a donut with one hole. He conjectured that the Willmore energy of a torus would always be greater than or equal to a certain minimum value. He also found that a particular surface, called the Clifford torus, realizes the minimal Willmore energy.

The Willmore energy is not only of theoretical interest but also arises in nature. In 1991, molecular biologists observed, under a microscope, that fluid-filled sacs in certain cells were Clifford tori. The sacs assumed that shape naturally, to minimize the Willmore energy.

In the decades after 1965, the Willmore conjecture stimulated a great deal of research, because of its naturalness and beauty and because of the richness of the concept of the Willmore energy. But it was not until the 2012 work of Codá-Marques and Neves that the Willmore conjecture was fully resolved. A major breakthrough came when they discovered the essential role played by the key feature of the surfaces in question: they have exactly one hole. The topology of the surfaces ended up playing a strong role in the geometric question the two mathematicians were exploring. In an interview to appear in the Notices of the AMS in the February 2016 issue, Codá Marques said, "It was pure topology, and it was beautiful."

As with many ground-breaking results in mathematics, the work of Codá Marques and Neves has illuminated new approaches to other significant questions, which they are actively pursuing.

Presented annually, the AMS Veblen Prize is one of the highest distinctions for research in topology and geometry. The prize will be awarded on Thursday, January 7, 2016, at the Joint Mathematics Meetings in Seattle.
-end-
Find out more about AMS prizes and awards at http://www.ams.org/prizes-awards/prizes.

American Mathematical Society

Related Mathematics Articles from Brightsurf:

A new method for boosting the learning of mathematics
How can mathematics learning in primary school be facilitated? UNIGE has developed an intervention to promote the learning of math in school.

Could mathematics help to better treat cancer?
Impaired information processing may prevent cells from perceiving their environment correctly; they then start acting in an uncontrolled way and this can lead to the development of cancer.

People can see beauty in complex mathematics, study shows
Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.

Improving geothermal HVAC systems with mathematics
Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.

How the power of mathematics can help assess lung function
Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.

Mathematics pushes innovation in 4-D printing
New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.

More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.

How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.

US educators awarded for exemplary teaching in mathematics
Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.

Authors of year's best books in mathematics honored
Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.

Read More: Mathematics News and Mathematics Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.