Ergodic theory, homogeneous dynamics, and applications to number theory (especially Diophantine problems).
I am currently an associate professor at the Morningside Center of Mathematics, Beijing, China.
Education:
2013/09-2019/06 Ph.D The Ohio State University, USA
2009/09-2013/06 B.S Peking University
Employment
1. 2019/09-2022/07, Hermann Weyl Instructor, ETH Zürich, Zürich, Switzerland
2. 2022/08-present, Associate Professor, Academy of Mathematics and Systems Science, Chinese Academy of Science.
Publications & Preprints:
1. Equidistribution of non-uniformly stretching translates of shrinking smooth curves and weighted Dirichlet approximation. [arxiv] (with N. Shah). Preprint.
2. A uniform Linnik basic lemma and entropy bounds. [arxiv] (with A. Wieser). Submitted.
3. Rational points on certain homogeneous varieties. [arxiv] Submitted.
4. Expanding translates of shrinking submanifolds in homogeneous spaces and Diophantine approximation. [arxiv] (with N. Shah). Submitted.
5. Equidistribution of expanding translates of curves and Diophantine approximation on matrices. [arxiv] Invent. Math. 220, pages 909-948 (2020).
6. Equidistribution in the space of 3-lattices and Dirichlet-improvable vectors on planar lines. [arxiv] (with D. Kleinbock, N. de Saxcé, N. Shah). Accepted by Ann. Scuola Norm. Super. Pisa.
7. Equidistribution of expanding degenerate manifolds in the space of lattices. [arxiv] (with N. Shah). Submitted.
研究方向
齐性动力系统与数论中的应用
教育经历
2009.09-2013.07 北京大学数学科学学院 本科
2013.08-2019.05 美国俄亥俄州立大学 博士
工作经历
2019.09-2022.08 瑞士苏黎世联邦理工学院 博士后
2022.09-至今 中国科学院数学与系统科学研究院 副研究员
文章与预印本
（1） Nimish Shah; Pengyu Yang; An upper bound of the Hausdorff dimension of singular vectors on affine subspaces, Transactions of the American Mathematical Society, Series B, 2024, 11(36)
（2） Nimish A. Shah; Pengyu Yang; Equidistribution of expanding degenerate manifolds in the space of lattices, Proceedings of the London Mathematical Society, 2024, 129(4)
（3） Nimish A. Shah; Pengyu Yang; Equidistribution of non-uniformly stretching translates of shrinking smooth curves and weighted Dirichlet approximation, Mathematische Zeitschrift, 2024, 308(4)
（4） Dmitry Kleinbock; Nicolas de Saxcé; Nimish A. Shah; Pengyu Yang; Equidistribution in the space of 3-lattices and Dirichlet-improvable vectors on planar lines, Annali della Scuola normale superiore di Pisa. Classe di scienze, 2024, XXV(1)
（5） Andreas Wieser; Pengyu Yang; A uniform Linnik basic lemma and entropy bounds, Comm. Math. Helv. To appear
（6）Pengyu Yang; Equidistribution of expanding translates of curves and Diophantine approximation on matrices, Inventiones mathematicae, 2020, 220(1): 909-948
