Robert Haslhofer
Assistant Professor University of Toronto, Department of Mathematics
University of Toronto, Department of Mathematics
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Research Interests
Accomplishments
ETH Medal
Awarded for outstanding doctoral thesis.
Silver Medal
Awarded at the 33rd International Physics Olympiad.
Silver Medal
Awarded at the 32nd International Physics Olympiad.
Education
ETH Zürich
Ph.D.
Mathematics
2012
ETH Zürich
M.Sc
Mathematics
2008
ETH Zürich
B.Sc
Mathematics
2006
Affiliations
- Canadian Mathematical Society
- American Mathematical Society
Links
Research Grants
NSERC Discovery Grant
National Science and Engineering Research Council of Canada
2016-2021
Mean curvature flow and Ricci flow
NSF Research Grant
National Science Foundation
2014-2017
Mean curvature flow and Ricci flow
Articles
The moduli space of 2-convex embedded spheres
preprint2016
We prove that the moduli space of 2-convex embedded n-spheres in R^{n+1} is path-connected for every n. Our proof uses mean curvature flow with surgery.
Characterizations of the Ricci flow
Journal of the European Mathematical Society (to appear)2016
This is the first of a series of papers, where we introduce a new class of estimates for the Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a notion of weak solutions to the Ricci flow in the nonsmooth setting.
Mean curvature flow with surgery
Duke Mathematical Journal (to appear)2016
We give a new proof for the existence of mean curvature flow with surgery of 2-convex hypersurfaces in arbitrary dimension, as announced in our previous paper.
Mean curvature flow of mean convex hypersurfaces
Communications in Pure and Applied Mathematics2016
In the present paper, we give a new treatment of the theory of mean convex (and k-convex) mean curvature flow, initially developed by White and Huisken-Sinestrari. This includes an estimate for derivatives of curvatures, a convexity estimate, a cylindrical estimate, a global convergence theorem, a structure theorem for ancient solutions, and a partial regularity theorem.
Quantitative Stratification and the Regularity of Mean Curvature Flow
Geometric and Functional Analysis2013
We adapt the quantitative stratification method to the parabolic setting, and use it to prove quantitative estimates and regularity results for weak solutions of the mean curvature flow.
A Compactness Theorem for Complete Ricci Shrinkers
Geometric and Functional Analysis2011
We prove precompactness in an orbifold Cheeger–Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound.
