Uploaded March 2026 | Updated September 2026, 3 weeks ago
Joint IAS/PU Symplectic Geometry Seminar
1:00pm|Simonyi 101 and Remote Access
Topic: Non-convex Hypersurfaces And Robust Heterodimensional Cycles
Speaker: Julian Chaidez
Affiliation: University of Southern California
Date: March 24, 02026
A closed hypersurface in a contact manifold is convex if it admits a transverse contact vector field. A closed hypersurface is robustly non-convex if it cannot be smoothly approximated by a convex hypersurface. The existence of such hypersurfaces was a longstanding open problem, resolved recently by myself using tools from partially hyperbolic dynamics.
In this talk, I will explain the relationship between robust non-convexity and the presence of a structure called a heterodimensional cycle in the characteristic foliation of the hypersurface. As an application, one can prove that any closed hypersurface in any contact manifold can be perturbed in the C0
-topology to a robustly non-convex hypersurface. This substantially generalizes and simplifies my previous work. This talk covers joint work with my PhD student Michael Huang (USC).
Joint IAS/PU Symplectic Geometry Seminar
1:00pm|Simonyi 101 and Remote Access
Topic: Non-convex Hypersurfaces And Robust Heterodimensional Cycles
Speaker: Julian Chaidez
Affiliation: University of Southern California
Date: March 24, 02026
A closed hypersurface in a contact manifold is convex if it admits a transverse contact vector field. A closed hypersurface is robustly non-convex if it cannot be smoothly approximated by a convex hypersurface. The existence of such hypersurfaces was a longstanding open problem, resolved recently by myself using tools from partially hyperbolic dynamics.
In this talk, I will explain the relationship between robust non-convexity and the presence of a structure called a heterodimensional cycle in the characteristic foliation of the hypersurface. As an application, one can prove that any closed hypersurface in any contact manifold can be perturbed in the C0
-topology to a robustly non-convex hypersurface. This substantially generalizes and simplifies my previous work. This talk covers joint work with my PhD student Michael Huang (USC).
