Prof.. Weixiao Shen, coauthored with Haojie Ren (his PhD student at Fudan University) a new research paper, which was published and appear online by one of the top-four mathematical journals Inventiones mathematicae. This is the seventh research paper, authored by researchers in Shanghai Center for Mathematical Sciences (in short SCMS), that appeared in one of the top-four mathematical journals.

The paper titled“A DICHOTOMY FOR THE WEIERSTRASS-TYPE FUNCTIONS ", it appeared in https://link.springer.com/article/10.1007/s00222-021-01060-2.

This paper concerns the fractal properties of Weierstrass-type functions. In the late 19th century, Weierstrass discovered functions that are continuous and nowhere differentiable. This discovery had influenced greatly the later development of mathematics. Naturally, this class of Weiertrass functions becomes one of the most studied object in fractal geometry. Determining the Hausdorff dimensions of the graphs of this class of functions becomes a longstanding open problem in the subject. In his prior paper, Dr. Shen determined the Hausdorff dimension of the graphs of the classical Weierstrass functions. In the mentioned paper, by using a more general periodic analytic function, he proved that either the resulting Weierstrass-type curve is analytic or its Hausdorff dimension is equal to an explicit constant greater than 1. Pushing further, he introduced the notion `regulating period’, and proved that certain transversality conditions hold unless the Weierstrass-type function is analytic. In the end, they suceeded in determining the desired Hausdorff dimension. This paper is an important progress in the famous problem of determining the Hausdorff dimension of Weierstrass-type functions.

Prof. Shen received his bachelor's degree from the University of Science and Technology of China (in short USTC) in 1996; received his Ph.D. from University of Tokyo in 2001. After, he worked as a postdoctoral fellow at Warwick University, and became a professor at USTC and the National University of Singapore. In 2015, Prof. Shen joined SCMS as a chair professor.

As an internationally renowned scholar in the field of Dynamic Systems, Prof. Shen won the S.S. Chern Prize from the Chinese Mathematical Society in 2009, he was the youngest recipient in the history of this prize. He was an invited speaker in the International Congress of Mathematicians in 2014.