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Faculty Member

Professor Jun Ling

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Office: LA 121 M
Mail Stop: 261

Biography

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Recent research

A New Differential Form And 6-Shere
https://hal.science/hal-05060123/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-05027695v1/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

MATH 4220

Advanced Calculus II, Spring 2025

MATH 1210

Calculus I QL, Spring 2025

MATH 1220

Calculus II, Spring 2025

MATH 2270

Linear Algebra, Spring 2025

Presentations

Ling, Jun Michael (Presenter & Author), AGAS, "Some properties of almost complex structures", Department of Mathematics at Cornell University, Cornell University, Ithaca, New York, USA. (March 20, 2023)

Ling, Jun (Presenter & Author), DGGA, "The Square of Nijenhuis Tensor and Its Vanishing Results ", Department of Mathematics at Princeton University, www.math.princeton.edu/events/archive. (October 26, 2022)

Scholarly/Creative Works

Ling, Jun , "A new differential form and 6-Shere" . https://hal.science/hal-05060123v1/document

Ling, Jun , "Integrabily And Cohomology And 6-Sphere" . https://hal.science/hal-05027695v1/document

Ling, Jun Michael , (2021) "The square of Nijenhuis tensor and its vanishing results" (vol. Online Ready). Asian-European Journal of Mathematics,.

Ling, Jun , (2011) "Estimate and monotonicity of the first eigenvalue under Ricci Flow (joint with X. Cao, S. Hou" (vol. 354}, pages 451–463(2012) ). Germany: Math. Ann. /Springer. https://link.springer.com/article/10.1007/s00208-011-0740-6

Ling, Jun , Bian, B. J., Li, S. H., Wang, X. J., (2010) "Trends in Partial Dierential Equations, Advanced Lectures in Mathematics 10" . International Press of Boston,.

Ling, Jun , (2008) "Estimates on the lower bound of the rst gap," (Issue: 3, vol. 16). Comm. Anal. Geometry,.

College Algebra QL, Spring 2006

MATH 1100

Introduction to Calculus QL, Spring 2006

Ling, Jun , (2007) "Annals of Global Analysis and Geometry" (Issue: 4, vol. 31). Lower bounds of the eigenvalues of compact manifolds with positive Ricci curvature.

Ling, Jun , (2006) "International Journal of Mathematics" (Issue: 5, vol. 17). A lower bound of the rst Dirichlet eigenvalue of a compact manifold with positive Ricci curvature.

Ling, Jun , (2006) "Proc. Amer. Math. Soc." (Issue: 10, vol. 134). The rst eigenvalue of a closed manifold with positive Ricci curvature.