I am currently working at Caltech as an assistant professor. I am also a Sloan research fellow. Previously, I completed my PhD in 2019 at Princeton University, I continued as a postdoc at UC Berkeley and was a Clay fellow from 2019 to 2024.

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  [a talk recording]

• 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

to appear in Invent. Math.

• Spherical volume and spherical Plateau problem, arXiv:2202.10636

to appear in Séminaire de théorie spectrale et géométrie

• 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