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, especially those which are optimal under natural constraints. In particular, many of my papers involve minimal surfaces and harmonic maps. Recently, I have started to explore their properties in high-dimensional spaces, and new connections with other fields like representation theory, geometric group theory, random matrices.
Here is my CV.
Email: aysong@caltech.edu
Random harmonic maps into 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
to appear in J. Eur. Math. Soc.
Entropy and stability of hyperbolic manifolds, arXiv:2302.07422
Geom. Funct. Anal., vol. 35, no. 3, pp. 877-914 (2025)
Stability of Euclidean 3-space for the Positive Mass Theorem, with Conghan Dong, arXiv:2302.07414
Invent. Math., vol. 239, no. 1, pp. 287-319 (2025)
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
Geom. Topol., vol. 28, pp. 1113-1152 (2024)
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
Duke Math. J., vol. 172, no. 11, pp. 2149-2193 (2023)
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
Ann. Sci. Ec. Norm. Supér., vol. 56, no. 4, pp. 1085-1134 (2023)
Existence of infinitely many minimal hypersurfaces in closed manifolds, arXiv :1806.08816
Ann. of Math., vol. 197, no. 3, pp. 859-895 (2023)
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