Réunion d'hiver SMC 2025
Toronto, 5 - 8 decembre 2025
Relativité mathématique et analyse géométrique
Org: Aghil Alaee (Clark University) et Hari Kundrui (McMaster University)
[PDF]
Org: Aghil Alaee (Clark University) et Hari Kundrui (McMaster University)
[PDF]
- AMIR BABAK AAZAMI, Clark University
- TRACEY BALEHOWSKY, University of Calgary
- IVAN BOOTH, Memorial University of Newfoundland
- GRAHAM COX, Memorial University of Newfoundland
- NISHANTH GUDAPATI, College of the Holy Cross
- JEFF JAUREGUI, Union College
- NIKY KAMRAN
Global counterexamples to uniqueness for a Calder\'on problem with $C^k$ conductivities [PDF]
- TRACEY BALEHOWSKY, University of Calgary
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Let $\Omega$ be a bounded subset of $\mathbb{R}^n$ with $C^{\infty}$ boundary, where $n\geq 3$, and let $\gamma=(\gamma^{ij})$ be a bounded measurable function on $\overline{\Omega}$ taking values in the set ${\mathcal S}_n$ of positive definite $n \times n$ symmetric matrices. The Calder\'on inverse problem consists in recovering the map $\gamma$ from the from the knowledge of the Dirichlet-to-Neumann map at fixed frequency for the operator $L_{\gamma}=-\partial_i (\gamma^{ij} \partial_j )$, up to some gauge equivalences induced by the invariance properties of the Dirichlet-to-Neumann map. We obtain counterexamples to uniqueness for the Calder\'on problem by showing that for any smooth map $\gamma$ and any frequency that does not belong to the Dirichlet spectrum of $L_{\gamma}$, there exists, for any $k\geq 1$ and any $\epsilon > 0$, a pair of non gauge-equivalent maps $\gamma_1, \gamma_2$ of class $C^k$ which are $\epsilon$-close to $\gamma$ in the $C^{k}(\overline{\Omega},{\mathcal S}_n)$ topology, such that their Dirichlet-to-Neumann maps are equal. This is joint work with Thierry Daudé (Besançon), Bernard Helffer (Nantes) and François Nicoleau (Nantes).
- MARIEM MAGDY, Perimeter Institute
- ARGAM OHANYAN, University of Toronto
On the geometry of continuously differentiable spacetime metrics [PDF]
- ARGAM OHANYAN, University of Toronto
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Nonsmooth metrics appear naturally in mathematical relativity and spacetime geometry, whether as solutions of Einstein's equations or during the course of physically relevant operations such as spacetime matching. It is important to study their geometry also to give further physical credence to the singularity theorems of Hawking and Penrose.
In this talk, we will discuss the class of continuously differentiable spacetime metrics, for which many important theorems have been established recently. After introducing the main approximation tools and methods of study, we will discuss important applications such as the Hawking and Penrose singularity theorems, the Hawking-Penrose singularity theorem, and the splitting theorem.
This talk is partly based on joint collaborations with Kunzinger, Schinnerl, Steinbauer and with Braun, Gigli, McCann, Sämann.
- YAKOV SHLAPENTOKH ROTHMAN, University of Toronto
- CHRISTOPHER STITH, University of Michigan
- RYAN UGNER, University of California, Berkeley
- JAMES WHEELER, University of Michigan
- ERIC WOOLGAR, University of Alberta
- CHRISTOPHER STITH, University of Michigan