Locus of Critical Points for Some Polynomial

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Haotian Xie
Zheng Yang


Given a polynomial with complex coefficients, the celebrated Gauss-Lucas's theorem and Marden's theorem offer us insights into the geometry of the locus of its critical points. In the following paper, the authors explore the geometry under certain restrictions of the roots of the polynomials. In particular, the authors identify some regions where all critical points do not occur.

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Author Biography

Zheng Yang, Sichuan University

Zheng Yang is an assistant professor at Sichuan University Pittsburgh Institute since 2018. Dr. Yang received a Ph.D. in Mathematics from University of Nebraska-Lincoln in 2015. Between 2015 and 2018, he worked at Miami University of Ohio as a visiting assistant professor. Dr. Yang’s research interests are in the field of commutative algebra. His recent research interests also include math education and data science.