Biography

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Recent research

A New Differential Form And 6-Shere
https://hal.science/hal-05060123v2/document

We construct a new differential form from arbitrary almost complex structures on smooth manifolds. As an application of this differential form we prove that 6-Sphere does not have complex structure. A preprint of these advances was completed on January 29, 2025, and submitted on January 31, 2025. A shorter version of the proof is available online as a preprint:
https://hal.science/hal-05027695v2/document

The question of whether the above 6-dimensional sphere is a complex manifold is generally called the Hopf problem. For discussions on the Hopf problem up to 2017, please refer to:
I. Agricola, G. Bazzoni, and O. Goertsches, On the history of the Hopf problem,, Differential Geometry and its Applications, 57(2018), 1--9.

There is also a series of in-depth discussions on the Hopf problem on MathOverFlow??
Is there a complex structure on the 6-sphere?
https://mathoverflow.net/questions/1973/is-there-a-complex-structure-on-the-6-sphere
Atiyah's May 2018 paper on the 6-sphere
https://mathoverflow.net/questions/304071/atiyahs-may-2018-paper-on-the-6-sphere
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Ph.D. in Mathematics
University at Buffalo, The State University of New York (SUNY)

Member, Mathematical Sciences Research Institute (MSRI)
Berkeley, California, Feb 2007 - May 2007

Visiting Fellow, Department of Mathematics
Princeton University, Aug 2022 - Jan 2023

Visiting Professor, Department of Mathematics
Cornell University, Jan 2023 - Jun 2023
https://math.cornell.edu/jun-michael-ling

Teaching
Cornell University
MATH 2130 Calculus III, Spring 2023
https://classes.cornell.edu/browse/roster/SP23/class/MATH/2130

Teaching

Presentations

Scholarly/Creative Works

Awards