Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
Suppose we are given a globally hyperbolic spacetime (M,g) solving the Einstein vacuum equations, and a timelike geodesic in M. I will explain how to construct, on any compact subset of M, a solution geps of the Einstein vacuum equations which is approximately equal to g far from the geodesic but near any point along the geodesic approximately equal to the metric of a Kerr black hole with mass meps. As an application, we can construct spacetimes which describe the merger of a very light black hole with a unit mass black hole, followed by the relaxation of the resulting single black hole to its equilibrium (Kerr or Kerr-de Sitter) state.
In this talk, we explore étale groupoids $G$ with a locally compact Hausdorff unit space $X$, where $G$ itself may not be globally Hausdorff. For such groupoids, the essential $C^*$-algebra $C_{\textrm{ess}}^*(G)$ offers a more suitable framework than the reduced $C^*$-algebra $C_r^*(G)$, as it captures additional structural nuances. Specifically, $C_{\textrm{ess}}^*(G)$ arises as a proper quotient of $C_r^*(G)$.
We introduce the concept of essential amenability for groupoids, a condition that is strictly weaker than (topological) amenability yet sufficient to guarantee the nuclearity of $C_{\textrm{ess}}^*(G)$. To establish this, we define a maximal version of the essential $C^*$-algebra and show that any function with dense cosupport must be supported within the set of "dangerous arrows”, that is, arrows that cannot be topologically separated.
This essential amenability framework characterizes the nuclearity of $C_{\textrm{ess}}^*(G)$ and establishes its isomorphism to the maximal essential $C^*$-algebra. Our results offer new insights into the interplay between groupoid structure and operator algebras, extending the utility of $C_{\textrm{ess}}^*(G)$ in non-Hausdorff settings. This is based on joint work with Diego Martinez.
3d mirror symmetry is a mysterious duality for certain pairs of hyperkähler manifolds, or more generally complex symplectic manifolds/stacks. In this talk, we will describe its relationships with 2d mirror symmetry. This could be regarded as a 3d analog of the paper Mirror Symmetry is T-Duality by Strominger, Yau and Zaslow which described 2d mirror symmetry via 1d dualities.
