I am currently working at Caltech as an assistant professor. I am also a Clay research fellow. Previously, I completed my PhD in 2019 at Princeton University, and continued as a postdoc at UC Berkeley.

My research is mostly in Differential Geometry and Geometric Analysis. I am broadly interested in shapes that are optimal under natural constraints. In particular, many of my papers involve minimal surfaces and related geometries. Recently, my efforts have focused on bridging minimal surface theory with other fields like representation theory, geometric group theory and random matrices.

Here is my CV.

Email: aysong@caltech.edu

Research

Random minimal surfaces in spheres, arXiv:2402.10287 

Hyperbolic groups and spherical minimal surfaces, arXiv:2402.10869 

Scalar curvature and volume entropy of hyperbolic 3-manifolds, with Demetre Kazaras and Kai Xu, arXiv:2312.00138

Entropy and stability of hyperbolic manifolds, arXiv:2302.07422

Stability of Euclidean 3-space for the Positive Mass Theorem, with Conghan Dong, arXiv:2302.07414

Spherical volume and spherical Plateau problem, arXiv:2202.10636

On certain quantifications of Gromov's non-squeezing theorem, with Kevin Sackel, Umut Varolgunes and Jonathan J. Zhu, arXiv:2105.00586,

to appear in Geom. Topol.

Essential minimal volume of Einstein 4-manifolds, arXiv:2103.05659  

Generic scarring for minimal hypersurfaces along stable hypersurfaces, with Xin Zhou, arXiv :2006.03038,

Geom. Funct. Anal., vol. 31, no. 4, pp. 948-980 (2021)

Morse index, Betti numbers and singular set of bounded area minimal hypersurfaces,  arXiv :1911.09166

to appear in Duke Math. J.

On the existence of minimal Heegaard surfaces, with Daniel Ketover and Yevgeny Liokumovich, arXiv :1911.07161

A dichotomy for minimal hypersurfaces in manifolds thick at infinity, arXiv :1902.06767,

to appear in Ann. Sci. Ec. Norm. Supér.

Existence of infinitely many minimal hypersurfaces in closed manifolds, arXiv :1806.08816

to appear in Ann. of Math.

Equidistribution of minimal hypersurfaces for generic metrics, with Fernando C. Marques and André Neves, arXiv :1712.06238

Invent. Math., vol. 216, pp. 423-443 (2019)

Appearance of stable spheres along the Ricci flow in positive scalar curvature, arXiv :1611.09747

Geom. Topol., vol. 23, no. 7, pp. 3501-3535 (2019)

Embeddedness of least area minimal hypersurfaces, arXiv :1511.02844,

J. Differential Geom., vol. 110, no. 2, pp. 345-377 (2018)

A maximum principle for self-shrinkers and some consequences, arXiv :1412.4755