Ailana Fraser

Ailana Margaret Fraser is a Canadian mathematician and professor of mathematics at the University of British Columbia. She is known for her work in geometric analysis and the theory of minimal surfaces. 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.

Early life and education Fraser was born in Toronto, Ontario. After postdoctoral studies at the Courant Institute of New York University, she taught at Brown University before moving to UBC.

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 Canadian Mathematical Society in 2012 In 2018 the Canadian Mathematical Society listed her in their inaugural class of fellows and in 2021 awarded her, along with Marco Gualtieri, the Cathleen Synge Morawetz Prize. In 2022 she was awarded a Simons Fellowship.

Personal life Fraser is the daughter of statistician Donald A. S. Fraser.

Major publications