2026 CMS Winter Meeting
Montreal, Dec 11 - 14, 2026
Differential Geometry and Mathematical Physics
Org: Eric Bahuaud (Seattle University) and Frédéric Rochon (UQÀM)
Org: Eric Bahuaud (Seattle University) and Frédéric Rochon (UQÀM)
- ARAM ALYOUSEF, University of Alberta
- ABDOU OUSSAMA BENABIDA, UBC
- FACUNDO CAMANO, Waterloo
- BENJAMIN FRIEDMAN, UQÀM
- CHRISTINE GUENTHER, Pacific University
- ROBERT HARRIS, UQÀM
- CHRIS KOTTKE, Reed College
- HARI KUNDURI, McMaster University
- KUAN-HUI LEE, McGill
- MAXENCE MAYRAND, University of Sherbrooke
- RUXANDRA MORARU, University of Waterloo
- TRISTAN OZUCH, MIT
- ERIC WOOLGAR, University of Alberta
Spacetime conformal boundary causal rigidity [PDF]
- ABDOU OUSSAMA BENABIDA, UBC
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A well-known boundary rigidity problem for Riemannian geometry asks whether a manifold-with-boundary, such that all geodesic chords have the same length, is necessarily a round hemisphere. It is, and therefore any chord leaving a given boundary point passes through that point's antipode. For Lorentzian geometry, we pose the following conformal boundary rigidity problem. If all light rays leaving a point p in the distant past (Penrose's conformal infinity) refocus at the same point q in the distant future, and if the same is true for all such p, is the spacetime conformal to a maximally symmetric spacetime? For example, if the spacetime is also asymptotically anti-de Sitter, is it actually anti-de Sitter (up to conformal transformations that preserve the asymptotics)? I will answer this question, assuming that the spacetime is also stationary, based on joint work with Gabriel Paternain. Time permitting, I will discuss joint work with Alex Sandhu and Giulio Sanzeni on the positive cosmological constant version of this problem.
- XUWEN ZHU, Northeastern University