I am a Boas Assistant Professor (postdoc) at Northwestern University (2023-), under the supervision of Aaron Brown. I completed my PhD at University of Michigan (2018-2023), under the supervision of Ralf Spatzier.
My research interest lies in differential geometry and dynamical systems. Recently, I am working on the following topics:
Bounded cohomology and simplicial volume of nonpositively curved spaces.
Absolute continuity of stationary measures.
Riemannian metrics with ergodic geodesic flow.
[arXiv, Journal] The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds. (joint with Xuezhang Chen and Liming Sun), Adv. Math. 358 (2019), 106854. arXiv:1805.09597.
[arXiv, Journal] An existence theorem on the isoperimetric ratio over scalar-flat conformal classes. (joint with Xuezhang Chen and Tianlin Jin), J. Differential Equations 269 (2020), no. 5, 4116–4136. arXiv:1910.01512.
[arXiv, Journal] Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric. To appear in Math. Ann. https://doi.org/10.1007/s00208-024-02941-6, arXiv: 2201.09175.
[arXiv, Journal] The Cayley hyperbolic space and volume entropy rigidity. Math Z. (2024), 306,4, arXiv: 2203.14418.
[arXiv] Nonpositively curved 4-manifolds with zero Euler characteristic. (joint with Chris Connell and Shi Wang), submitted. arXiv:2309.15766. 17 pages. preprint.
[arXiv] Absolute continuity of stationary measures. (joint with Aaron Brown, Homin Lee and Davi Obata), arXiv:2409.18252. 34 pages. preprint.
[arXiv] Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one. (joint with Chris Connell and Shi Wang), arXiv:2410.19981. 166 pages. preprint.
*ArXiv versions may differ significantly from the published version.
Teaching at University of Michigan:
Math 105 Data, Functions and Graphs: Instructor (Fall 2018);
Math 115 Calculus I: Instructor (Winter 2019, Fall 2020, Fall 2021, Fall 2022);
Math 116 Calculus II: Instructor (Winter 2020);
Math 216 Differential Equations: Lab Instructor (Fall 2019).
Teaching at Northwestern University:
Math 220-2 Single Variable Integral Calculus(Winter 2024, Spring 2024, Fall 2024)
Math 230-1 Multivariable Differential Calculus (Winter 2025)
''Boundary rigidity and filling minimality via the barycenter method'', Differential Geometry seminar, Heidelberg University, Summer 2023. (Virtual)
''Boundary rigidity and filling minimality via the barycenter method'', Dynamics seminar, Northwestern University, Winter 2023.
"Filling volume minimality and boundary rigidity of metrics close to a rank-1 symmetric metric", Semi-annual Workshop in Dynamical Systems and Related Topics, Anatole Katok Center for Dynamical Systems and Geometry, Pennsylvania State University, Fall 2022.
''Boundary rigidity and filling minimality'', Geometry seminar, University of Michigan, Fall 2021.
''Thermodynamic formalism'', Graduate student mini-courses, University of Michigan, Summer 2022.
Email: ruanyp@northwestern.edu, ruanyp@umich.edu
Office: Lunt Hall 311