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Robert Haslhofer - University of Toronto, Department of Mathematics. Toronto, ON, CA

Robert Haslhofer Robert Haslhofer

Assistant Professor | University of Toronto, Department of Mathematics

Toronto, ON, CANADA

Robert Haslhofer's research focuses on geometric analysis

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Research

Research Interests (7)

Geometric Analysis

Geometric Flows

Differential Geometry

Partial Differential Equations

Calculus of Variations

Stochastic Analysis

General Relativity

Accomplishments (3)

ETH Medal (professional)

Awarded for outstanding doctoral thesis.

Silver Medal (professional)

Awarded at the 33rd International Physics Olympiad.

Silver Medal (professional)

Awarded at the 32nd International Physics Olympiad.

Education (3)

ETH Zürich: Ph.D., Mathematics 2012

ETH Zürich: M.Sc, Mathematics 2008

ETH Zürich: B.Sc, Mathematics 2006

Affiliations (2)

  • Canadian Mathematical Society
  • American Mathematical Society

Research Grants (2)

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 (6)

The moduli space of 2-convex embedded spheres preprint

2016 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.

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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.

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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.

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Mean curvature flow of mean convex hypersurfaces Communications in Pure and Applied Mathematics

2016 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.

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Quantitative Stratification and the Regularity of Mean Curvature Flow Geometric and Functional Analysis

2013 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.

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A Compactness Theorem for Complete Ricci Shrinkers Geometric and Functional Analysis

2011 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.

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