I am an Assistant Professor in the Center for Applied Mathematics at Tianjin University. My research lies in algebraic topology and homotopy theory, with an emphasis on computational stable homotopy theory. My name in Chinese is 张宇.
Ph.D. in Mathematics (2014–2020)
The Ohio State University, Columbus, Ohio, USA
Dissertation Advisor: John E. Harper
B.S. in Mathematics (2010–2014)
Peking University, Beijing, China
Dissertation Advisor: Huijun Fan
Research Interests
My research program is organized around the following themes:
Computational stable homotopy theory: Computer-assisted computation of Adams spectral sequences and stable homotopy groups of spheres at odd primes
Spectral sequences: Development, explicit calculation, and applications of spectral sequences in homotopy theory
Higher structures: Model categories and higher algebraic structures in stable homotopy theory
Structured ring spectra: Homotopy theory of structured ring spectra and their applications
Current focus: Developing computer programs for Adams spectral sequence calculations at odd primes, together with interactive tools for exploring the results.
Adams \(E_2\) Charts
This interactive visualization displays the Adams spectral sequence \(E_2\) page for the sphere spectrum \(S^0\) at odd primes. The computations use computer programs developed jointly with Weinan Lin. This work is ongoing, and the charts will be updated as our research progresses.
Choose a prime above to open its chart. These bounds refer to the internal degree \(t\); the charts plot the stem \(t-s\) horizontally and the Adams filtration \(s\) vertically.
Features:
Interactive zoom and pan navigation
Canonical monomial labels for selected basis elements
Visualization of multiplication support by \(x_0\) and \(x_1\) (classically \(a_0\) and \(h_0\))
Visualization Guide:
Bullets: Represent additive basis elements in the \(E_2\) page
Black lines: Show the combined multiplication support by \(x_0\) and \(x_1\); coefficients and multiplier labels are not displayed
Pan: Click and drag, or use arrow keys
Zoom: Mouse wheel, pinch gesture, or +/- keys
Select element: Click on any bullet to see its canonical monomial name and its product targets highlighted in green
Clear selection: Click empty chart space or select a different prime
Publications
The secondary periodic element \(\beta_{p^2/p^2-1}\) and its applications. Joint with J. Hong and X. Wang. Sci. China Math. 68, 207-222 (2025). SharedIt link | journal
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. Proc. Amer. Math. Soc. 152 (2024), 4521-4536. pdf | journal
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 \(BPU_n\) 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 | SharedIt link | journal
The \(p\)-primary subgroups of the cohomology of \(BPU_n\) 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
The 2023 Topology and its Applications Conference was held from May 12 to May 16, 2023, at Nankai University in Tianjin.
Algebraic topology has seen significant advances in recent years, and topological methods have found applications in fields ranging from chemistry and structural biology to social network analysis. This conference brought together researchers in topology and applied topology to share recent results and promote further development of the field.
An intuitive introduction to motivic homotopy theory
In May and June of 2021, I gave an online lecture series on motivic homotopy theory. The lectures provide an accessible introduction to the foundational setup and core concepts of the subject, aimed at an audience with a background in homotopy theory.
Lecture Materials:
Lecture 1: Overview, Category theory, and Simplicial sets. Slides