The Canadian Mathematical Society (CMS) is pleased to announce that Dr. Qin Deng (Massachusetts Institute of Technology) has been named the 2022 CMS Blair Spearman Doctoral Prize recipient. Dr. Deng will receive his award at the CMS Winter meeting in Toronto, Ontario.
Qin Deng is an outstanding researcher working in metric and Riemannian geometry as well as geometric analysis. Deng’s thesis contains a solution to a long-standing open problem in the theory of manifolds with lower Ricci curvature bounds and RCD spaces.
In the mid-1990s, Cheeger and Colding carried out a research program to understand the structure of spaces that arose as Gromov-Hausdorff limits of smooth Riemannian manifolds with Ricci curvature uniformly bounded from below, dimension uniformly bounded from above, and diameter uniformly bounded from above. These are natural objects of study when considering the basic rigidity theorems for manifolds of non-negative or positive Ricci curvature with the results of Cheeger and Colding quantitatively generalizing them.
A natural research direction has been to generalize the Cheeger-Colding results to the RCD setting. A combined community effort settled these problems in the affirmative, except for the Hölder continuity of tangent cones along geodesics. Deng’s thesis settled this important case and developed new tools for computing the change in distance along the flow of a vector field in the non-smooth setting. Moreover, Deng proved the non-branching property for RCD spaces, which states that two geodesics that coincide for a small interval cannot come apart. This property is an important tool for obtaining some of the more desirable properties possessed by Riemannian manifolds in these new settings. Furthermore, an integral version of the second-order variation formula for regular Lagrangian flows in the RCD setting was obtained. The results in Deng’s thesis may be viewed as a generalization of the breakthrough work of Colding and Naber on Hölder continuity of tangent cones, the latter appearing in the Annals of Mathematics in 2012. The thesis demonstrates Deng’s ability to assimilate a wide variety of deep, technical results and originality in combining them to make substantial advances.
Deng received his PhD from the University of Toronto in 2021 under the supervision of Vitali Kapovitch. The recipient of several awards such as the Ida Bulat Teaching Award, Malcolm Slingsby Robertson Prize, George F.D. Duff Graduate Fellowship, and an NSERC Alexander Graham Bell Canada Graduate Scholarship, Deng is now a C.L.E. Moore Instructor at the Massachusetts Institute of Technology.
The CMS Blair Spearman Doctoral Prize recognizes outstanding performance by a doctoral student. The prize is awarded to one or two recipients of a Ph.D. from a Canadian university whose overall performance in graduate school is judged to be the most outstanding. Although the dissertation will be the most important criterion (the impact of the results, the creativity of the work, the quality of exposition, etc.) it will not be the only one. Other publications, activities in support of students and other accomplishments will also be considered.
The CMS is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including: scientific meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements.
For more information, please contact:
|Dr. Termeh Kousha
Canadian Mathematical Society
||Dr. Anthony Bonato (Toronto Metropolitan University)
Chair, Doctoral Prize Selection Committee
Canadian Mathematical Society