Ailana Margaret Fraser is a Canadian mathematician and professor of mathematics at the

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

. She is known for her work in geometric analysis and the theory of minimal surfaces.UBC Mathematician Recognized for Research Excellence: Ailana Fraser to Receive CMS 2012 Krieger-Nelson Prize

Canadian Mathematical Society The Canadian Mathematical Society (CMS) (french: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the ...

, April 12, 2012, retrieved 2013-01-21. Her research is particularly focused on extremal

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

problems and sharp eigenvalue estimates for surfaces, min-max minimal surface theory, free boundary minimal surfaces, and positive isotropic curvature.

Early life and education

Fraser was born in

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

Ontario Ontario ( ; ) is one of the thirteen provinces and territories of Canada.Ontario is located in the geographic eastern half of Canada, but it has historically and politically been considered to be part of Central Canada. Located in Central Ca ...

. She received her Ph.D. from Stanford University in 1998 under the supervision of

Richard Schoen Richard Melvin Schoen (born October 23, 1950) 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. Career Born in Celina, Ohio, and a 1 ...

. After postdoctoral studies 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 ...

, she taught at

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

before moving to UBC.

Major work

Fraser is well-known for her 2011 work with Schoen on the first "Steklov eigenvalue" of a compact Riemannian manifold-with-boundary. This is defined as the minimal nonzero eigenvalue of the "Dirichlet to Neumann" operator which sends a function on the boundary to the normal derivative of its harmonic extension into the interior. In the two-dimensional case, Fraser and Schoen were able to adapt Paul Yang and Shing-Tung Yau's use of the Hersch trick in order to approximate the product of the first Steklov eigenvalue with the length of the boundary from above, by topological data. Under an ansatz of rotational symmetry, Fraser and Schoen carefully analyzed the case of an annulus, showing that the metric optimizing the above eigenvalue-length product is obtained as the intrinsic geometry of a geometrically meaningful part of the catenoid. By use of the uniformization theorem for surfaces with boundary, they were able to remove the condition of rotational symmetry, replacing it by certain weaker conditions; however, they conjectured that their result should be unconditional. In general dimensions, Fraser and Schoen developed a "boundary" version of Peter Li and Yau's "conformal volume." By building upon some of Li and Yau's arguments, they gave lower bounds for the first Steklov eigenvalue in terms of conformal volumes, in addition to isoperimetric inequalities for certain minimal surfaces of the unit ball.

Awards and honors

Fraser won the Krieger–Nelson Prize of the

in 2012 and became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2013. In 2018 the

listed her in their inaugural class of fellows and in 2021 awarded her, along with Marco Gualtieri, the

Cathleen Synge Morawetz Cathleen Synge Morawetz (May 5, 1923 – August 8, 2017) was a Canadian mathematician who spent much of her career in the United States. Morawetz's research was mainly in the study of the partial differential equations governing fluid flow, parti ...

Prize. In 2022 she was awarded a Simons Fellowship.

Major publications

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References

{{DEFAULTSORT:Fraser, Ailana Year of birth missing (living people) Living people Canadian mathematicians Canadian women mathematicians Women mathematicians Stanford University alumni Brown University faculty Academic staff of the University of British Columbia Fellows of the American Mathematical Society Fellows of the Canadian Mathematical Society Scientists from Toronto Courant Institute of Mathematical Sciences alumni