The 40th Anniversary of Shenzhen University and the 40th Anniversary of Mathematics Department

Liyuan scholar Colloquium forty-night

Lecture Title: Upper bound estimates of eigenvalues for Hormander operators on non-equiregular sub-Riemannian manifolds

Speaker: Prof. Hua Chen (Wuhan University)

Lecture time: November 7, 2023 15：30-16:30

Lecture location: Classroom No. 3, 1/F, Hui Xing Building, Yuehai Campus, Shenzhen University, China

Overview: In this talk, we shall study the closed eigenvalue problem and Dirichlet eigenvalue problem of self-adjoint Hormander operators on non-equiregular sub-Riemannian manifolds. By Rayleigh-Ritz formula and the subelliptic heat kernel estimates, we establish the upper bounds of eigenvalues which depend on the volume of the subunit ball and the measure of the manifold. Under a certain condition, we obtain the explicit upper bounds of eigenvalues which have the polynomially growth in k with the optimal order related to the non-isotropic dimension of the manifold.

Speaker Introduction: Chen Hua, professor, doctoral supervisor, School of Mathematics and Statistics, Wuhan University, winner of the National Outstanding Youth Fund, member of the sixth and seventh Subject Mathematics Evaluation Group of The State Council, member of the third Science and Technology Committee of the Ministry of Education. He is currently the director of the Collaborative Innovation Center for Mathematics of Wuhan University and the chairman of the Hubei Mathematical Society. Chen Hua's research interests include the theory of microlocal analysis of partial differential equations, degenerate partial differential equations and spectral theory of partial differential equations. So far, he has hosted a number of key projects of the National Natural Science Foundation, and has been a member of the 973 core mathematics project team of the National major project and won the cross-century Outstanding Talents Fund of the Ministry of Education. Chen Hua has published more than 120 papers in the international professional SCI mathematics journal, and has won the second prize of Science and Technology Progress twice by the National Ministry of Education. In 2017, the scientific research project he presided over won the first prize of the Natural Science Award of the National Ministry of Education.

Teachers and students are welcome to participate!

Invited by: School of Mathematical Sciences

School of Mathematical Sciences

November 2, 2023