Ruìān Chén

Math Ph.D. Candidate
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48109-1043
Office: East Hall 1836
Phone: (734)763-2592
Email: ruchen AT umich DOT edu
Curriculum Vitae.

Research Interests

  • Algebraic topology
    • Homotopy theory
      • Stable homotopy
      • Sheaf homotopy
  • Category theory
    • Higher category
    • Topos theory

Advisor: Igor Kriz.

Currently, I am working on the foundations and applications of E-rings and modules on sheaves.

Writings

Preprint

C.; Kriz, Igor; Pultr, Aleš. Kan's combinatorial spectra and their sheaves revisited. Theory Appl. Categ. 32, 1363-1396 (2017) (arXiv)
C.; Kriz, Igor; Pultr, Aleš. Rings and modules in Kan spectra. Submitted. (manuscript)

Other articles and notes

Translation of Verdier's original paper on Verdier duality: pdf.
Translation of Bertrand Toën's master course on algebraic stacks: pdf.
Notes on ∞-stacks as simplicial presheaves: pdf; exerpt of Toën & Vezzosi's article on homotopical algebraic geometry.
Notes of Julie Bergner's lecture series on 2-Segal spaces delivered at YTM 2019: pdf.

Teaching

Fall 2015: Graduate Student Instructor of Math 105: Data, Functions & Graphs, coordinated by Dr. Fernando Carreon.
Winter 2016: GSI of Math 115: Calculus I, coordinated by Dr. Angela Kubena.
Fall 2016: GSI of Math 116: Calculus II, coordinated by Dr. Paul Kessenich.
Winter 2017: GSI of Math 116, coordinated by Angela.
Fall 2017: GSI of Math 116, coordinated by Angela.
Spring 2018: GSI of Math 116, co-coordinated with Dr. Evangelos Dimou.
Fall 2018: Teaching Assistant of Math 215: Calculus I for Prof. Divakar Viswanath.
Winter 2019: Co-coordinator of Math 116, coordinated by Dr. Hanna Bennett.