Shrey Aryan

I am a fourth year graduate student in mathematics at MIT, advised by Prof. Tobias Colding. My research interests include geometric analysis, nonlinear PDEs, and optimal transport.

Before coming to MIT, I completed my master’s degree at ETH Zürich under the supervision of Prof. Alessio Figalli, and my undergraduate studies at École Polytechnique under the supervision of Prof. Yvan Martel.

Recent Preprints

Geometric Analysis

  1. Topological Bernstein Theorems for Minimal Hypersurfaces in $\mathbb{R}^4$ confined in space (with Alexander McWeeney). [pdf]

  2. On the Calabi–Yau Conjectures for Minimal Hypersurfaces in Higher Dimensions (with Alexander McWeeney).[pdf]

Nonlinear PDEs

  1. Continuous in time bubbling and Soliton Resolution for Non-negative Solutions of the Energy-Critical Heat Flow. [pdf]

  2. Soliton resolution for the energy-critical nonlinear heat equation in the radial case. To appear in Analysis & PDE. [pdf]

Optimal transport

  1. Spectral Obstructions to Contracting Transport Maps on Curved Spaces. [pdf]

  2. Entropic Selection Principle for Monge’s Optimal Transport (with Promit Ghosal). [pdf]

See here for a complete publications list.