Yu Zhang - TJU Homepage

About me



My name in Chinese is 张宇.

I am currently an Assistant Professor at the Center for Applied Mathematics, Tianjin University.

My primary research focuses on algebraic topology, specifically in homotopy theory.

For more detailed information about my background, please refer to my CV, 中文简历.

This homepage was last updated on September 14, 2023.

Employment

  • Assistant Professor (2023--present), Tianjin University, Tianjin, China.

  • Postdoctoral Researcher (2020--2023), Nankai University, Tianjin, China.

    • Education

  • The Ohio State University (2014--2020), Columbus, Ohio, USA
    Ph.D. in Mathematics, Dissertation Advisor: John E. Harper

  • Peking University (2010--2014), Beijing, China
    B.S. in Mathematics, Dissertation Advisor: Huijun Fan



    • Research



    Research Area: Algebraic topology. More specifically, I am interested in classical and motivic homotopy theory computing the stable homotopy groups of spheres; model categories and higher category theory; and higher structures of spaces and ring spectra.

    Publications/preprints


  • The secondary periodic element $\beta_{p^2/p^2-1}$ and its applications.
    (joint with J. Hong and X. Wang). Submitted for publication. pdf

  • Detecting nontrivial products in the stable homotopy ring of spheres via the third Morava stabilizer algebra.
    (joint with X. Wang, J. Wu, and L. Zhong). Submitted for publication. pdf

  • A correspondence between higher Adams differentials and higher algebraic Novikov differentials at odd primes.
    (joint with X. Wang). Proc. Amer. Math. Soc. 151 (2023), 5087-5096. pdf / journal

  • The p-primary subgroup of the cohomology of BPUn in dimension 2p+6.
    (joint with Z. Zhang, L. Zhong). Topology Appl. 338 (2023): 108642. pdf / journal

  • Some nontrivial secondary Adams differentials on the fourth line.
    (joint with X. Wang and Y. Wang). New York J. Math. 29 (2023) 687–707. pdf / journal

  • Homotopy pro-nilpotent structured ring spectra and topological Quillen localization.
    J. Homotopy Relat. Struct. 17, 511–523 (2022). pdf / journal

  • The p-primary subgroups of the cohomology of BPUn in dimensions less than 2p+5.
    (joint with X. Gu, Z. Zhang and L. Zhong). Proc. Amer. Math. Soc. 150 (2022), 4099–4111. pdf / journal

  • Topological Quillen localization of structured ring spectra.
    (joint with J. Harper). Tbilisi Mathematical Journal 12(3):69–91, 2019. pdf / journal

    • Conference

    2023 Topology and its Applications Conference

    We are pleased to announce the upcoming 2023 Topology and its Applications Conference, scheduled from May 12 to May 16 at Nankai University in Tianjin.

    Algebraic topology, an important branch of mathematics, has witnessed significant progress in recent years. Topology has also found useful applications in fields such as chemical compounds, biological proteins, and social networks for data analysis. This conference aims to bring together distinguished experts in the field of topology and applied topology, promoting the development of topological applications and providing a platform for sharing insights and research findings on the latest advancements in this area.

    For further information about the conference, please visit the conference website.

    Lecture

    An intuitive introduction to motivic homotopy theory

    In May and June of 2021, I gave an online lecture series on motivic homotopy theory. This is intended to be a leisure introduction to the most basic setup and relavant concepts in motivic homotopy theory, from a homotopy theorist's point of view. The slides are given here. Please be warned that these informal notes might contain mistakes.

    Lecture 1: Overview, Category theory, and Simplicial sets. Slides

    Lecture 2: Model category. Slides

    Lecture 3: Scheme. Slides

    Lecture 4: Unstable motivic homotopy theory. Slides

    Lecture 5: Stable motivic homotopy theory. Slides

    Videos of the lectures are available for download here. Password: hny3

    The lectures were given in Chinese.


    Teaching

    As instructor at NKU

    Probability and Statistics for Liberal Arts, Spring 2022.

    Advanced Mathematics for Liberal Arts, Autumn 2021.

    As graduate teaching associate at OSU

    Math 2177: Mathematical Topics for Engineers, Autumn 2018.

    Math 1172: Engineering Mathematics A, Autumn 2017.

    Math 1172: Engineering Mathematics A, Autumn 2016.

    Math 1152: Calculus II, Spring 2016.