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Ailana M. Fraser



Department of Mathematics
University of British Columbia
121 - 1984 Mathematics Road
Vancouver, BC V6T 1Z2

Email: afraser@math.ubc.ca
Phone: (604) 822-2785
Fax: (604) 822-6074

Office: Math Annex 1226

Research: Differential Geometry, Geometric Analysis

Selected Honours:

CMS 2021 Catheeen Morawetz Synge Prize

Fellow of the Canadian Mathematical Society, 2018-

Fellow of the American Mathematical Society, 2012-

CMS 2012 Krieger-Nelson Prize

NSERC Discovery Accelerator Supplement, 2010-2013

NSERC University Faculty Award, 2002-2007

Recent Events Co-organized:

2020 CMS 75th Anniversary Summer Meeting, Ottawa (online), June 7-11, 2021

Connecting Women in Mathematics Across Canada (CWiMAC), Ottawa (online), June 2-3, 2021

PIMS Workshop on Geometric Anlaysis, UBC, May 18-19, 2019

Pacific Northwest Geometry Seminar, UBC, March 3-4, 2018

PIMS CRG Conference on Geometric Analysis, UBC, July 24-28, 2017

CMS Winter Meeting, Session on Differential Geometry, Montreal, Dec 4-7, 2015

Women in Geometry Workshop held at Banff International Research Station, November 1-6, 2015. Here is the Women in Geometry Workshop webpage.

Selected Publications:

Existence and classification of S^1-invariant free boundary annuli and Mobius bands in B^n (with P. Sargent), The Journal of Geometric Analysis 31 (2021), 2703-2725.

Some results on higher eigenvalue optimization (with R. Schoen), Calculus of Variations and Partial Differential Equations 59 (2020), no. 5, 22pp.

Extremal eigenvalue problems and free boundary minimal surfaces in the ball, Lecture Notes in Mathematics, Springer / Fondatione C.I.M.E. 2263 (2020), 1-40.

Existence of harmonic maps into CAT(1) spaces (with C. Breiner, L.-H. Huang, C. Mese, P. Sargent, Y. Zhang), Communications in Analysis and Geometry 28> (2020), no.4 781-835. Special issue in honor of Prof. K. Uhlenbeck's 75th birthday.

Shape optimization for the Steklov problem in higher dimensions (with R. Schoen), Advances in Mathematics 348 (2019), 146-162.

Regularity of Harmonic Maps from Polyhedra to CAT(1) Spaces (with C. Breiner, L.-H. Huang, C. Mese, P. Sargent, Y. Zhang), Calculus of Variations and Partial Differential Equations 57 (2018), no. 1, 1-35.

Mean curvature in manifolds with Ricci curvature bounded from below (with J. Choe), Commentarii Mathematici Helvetici 93 (2018), no.1, 55-69.

Sharp eigenvalue bounds and minimal surfaces in the ball (with R. Schoen), Inventiones Mathematicae 203(3) (2016), 823-890.

Uniqueness theorems for free boundary minimal disks in space forms (with R. Schoen), International Mathematics Research Notices (2015), no. 17, 8268-8274.

Minimal immersions of compact bordered Riemann surfaces with free boundary (with J. Chen, C. Pang), Transactions of the American Mathematical Society 367 (2015), 2487-2507.

Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with non-negative Ricci curvature and convex boundary (with M. Li), Journal of Differential Geometry 96 (2014), no.2, 183-200.

Minimal surfaces and eigenvalue problems (with R. Schoen), Contemporary Mathematics 599 (2013), 105-121.

Minimal surface techniques in Riemannian geometry, Surveys in Geometric Analysis and Relativity, Advanced Lectures in Mathematics 20, International Press (2011), 205-219.

The first Steklov eigenvalue, conformal geometry, and minimal surfaces (with R. Schoen), Advances in Mathematics 226 (2011), no. 5 4011-4030.

Holomorphic variations of minimal disks with boundary on a Lagrangian surface (with J. Chen), Canadian Journal of Mathematics 62 (2010), no. 6 1264-1275.

On stable minimal disks in manifolds with nonnegative isotropic curvature (with J. Chen), Journal fur die Reine und Angewandte Mathematik 643 (2010), 21-37.

Index estimates for minimal surfaces and k-convexity, Proceedings of the American Mathematical Society 135 (2007), no. 11 3733-3744.

The fundamental group of manifolds of positive isotropic curvature and surface groups (with J. Wolfson), Duke Mathematical Journal 133 (2006), no.2 325-334.

Fundamental groups of manifolds with positive isotropic curvature, Annals of Mathematics 158 (2003), no. 1 345-354.

Minimal disks and two-convex hypersurfaces, American Journal of Mathematics 124 (2002), no.3 483-493.

On the free boundary variational problem for minimal disks, Communications on Pure and Applied Mathematics 53 (2000), no. 8 931-971.