[4] Y. Zhang, The stacky approach to de Rham-Witt cohomology. In preparation.
research
My current interests center on the relationship between the classical work of Ekedahl, Illusie–Raynaud, and Nygaard and modern developments in p-adic geometry. I am particularly interested in how de Rham-Witt cohomology, the slope spectral sequence, dominoes, and F-gauges can be understood through the stacky approach to prismatic cohomology.
I am also interested in topics in positive-characteristic algebraic geometry, such as Ekedahl–Oort stratifications, p-primary Brauer groups, and K3 surfaces.
Recently, I have also become interested in q-de Rham cohomology, Habiro cohomology, and even filtrations, especially their connections with arithmetic geometry and homotopy theory.
Before graduate school, I worked on algebraic combinatorics, especially Schubert calculus, k-Schur functions, and q-analogues.
I also enjoy creating mathematical visualizations through vibe coding with the help of Codex and Claude Code; some of these projects can be found in the gallery.
writing
[3] Y. Zhang, Harder-Narasimhan filtration of torsion F-gauges. [arXiv:2609]
[2] Y. Zhang, Higher dimensional dominoes in de Rham-Witt cohomology. [arXiv:2607]
[1] The 2020 Polymath Jr. REU “q-binomials and the Grassmannian group”, Filtering cohomology of ordinary and Lagrangian Grassmannians. [arXiv:2011]
notes
q-de Rham cohomology and Habiro rings. [PDF]
seminars & talks
Harder-Narasimhan filtration of torsion F-gauges, Student arithmetic geometry seminar, Berkeley.
q-de Rham cohomology and Habiro rings, SLMath mini workshop. [event page] [notes]
q-de Rham cohomology and Habiro rings. A mini workshop on q-de Rham cohomology and Habiro rings that I organized at SLMath in September 2026, bringing together arithmetic geometry and quantum topology. [seminar page]
SLMath graduate student seminar. A graduate student seminar and mini workshops that I co-organize with Erika Beserra at SLMath in Fall 2026. [seminar page]
From F-crystals to Hodge–Witt cohomology, IU–Purdue Joint Workshop on Prismatic F-gauges. [event page]
Nygaard filtered prismatization in mixed characteristics, IU–Purdue Arithmetic Geometry Learning Seminar. [event page]
Prismatic F-gauges learning seminar. A learning seminar on prismatic F-gauges that I organized during Winter and Spring 2024. [seminar page]