Ailana Fraser

Source: Wikipedia, the free encyclopedia.
Ailana Margaret Fraser
Born
Toronto, Ontario, Canada
OccupationProfessor of Mathematics
Academic background
Alma materStanford University
Academic work
DisciplineMathematics, Geometric Analysis
InstitutionsUniversity of British Columbia

Ailana Margaret Fraser is a Canadian mathematician and professor of mathematics at the University of British Columbia.[1] She is known for her work in geometric analysis and the theory of minimal surfaces.[2] Her research is particularly focused on extremal eigenvalue problems and sharp eigenvalue estimates for surfaces, min-max minimal surface theory, free boundary minimal surfaces, and positive isotropic curvature.[3]

Early life and education

Fraser was born in

Courant Institute of New York University, she taught at Brown University before moving to UBC.[2]

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.[5][6]

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."[7] 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 Canadian Mathematical Society in 2012[2] and became a fellow of the American Mathematical Society in 2013.[8] In 2018 the Canadian Mathematical Society listed her in their inaugural class of fellows[9] and in 2021 awarded her, along with Marco Gualtieri, the Cathleen Synge Morawetz Prize.[10] In 2022 she was awarded a Simons Fellowship.[11]

Major publications

  • Fraser, Ailana;
    Zbl 1215.53052
    .
  • Fraser, Ailana;
    Zbl 1337.35099
    .

References

  1. ^ Faculty listing Archived 2020-08-10 at the Wayback Machine, UBC Mathematics, retrieved 2013-01-21.
  2. ^ a b c d e UBC Mathematician Recognized for Research Excellence: Ailana Fraser to Receive CMS 2012 Krieger-Nelson Prize, Canadian Mathematical Society, April 12, 2012, retrieved 2013-01-21.
  3. ^ "Ailana Fraser". Institute for Advanced Study. Retrieved 2019-03-12.
  4. ^ Ailana Margaret Fraser at the Mathematics Genealogy Project.
  5. Zbl 0224.73083
    .
  6. Zbl 0446.58017
    .
  7. Zbl 0503.53042
    .
  8. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-21.
  9. ^ Canadian Mathematical Society Inaugural Class of Fellows, Canadian Mathematical Society, December 7, 2018
  10. ^ Professors Ailana Fraser and Marco Gualtieri to receive the 2021 CMS Cathleen Synge Morawetz Prize, Canadian Mathematical Society, February 10, 2021
  11. ^ "2022 Simons Fellows in Mathematics and Theoretical Physics Announced". Simons Foundation. 2022-02-18. Retrieved 2022-07-04.
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