February 18, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/11:30 pm Beijing)
Speaker: Ryo Toyota (Texas A&M University) Recording
Title: Higher Index Theory for Relatively Hyperbolic Groups
Abstract: Higher index theory extends the Atiyah-Singer index theorem to non-compact manifolds and is closely related to scalar curvature and operator algebras. A central tool in this framework is the coarse Baum-Connes conjecture, which claims an algorithm for computing higher indices. In this talk, we will introduce a twisted version of the coarse Baum-Connes conjecture and show that it enjoys stronger permanence properties, such as under taking subspaces and finite unions. Then we apply this machinery to show that for a relatively hyperbolic group, it satisfies the twisted coarse Baum-Connes conjecture if and only if each peripheral subgroup does. The preprint is available at arXiv:2509.06876.
March 04, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/11:30 pm Beijing)
Speaker: Mathias Braun (EPFL) Recording
Title: Spacetime reconstruction and measured Lorentz-Gromov-Hausdorff convergence
Abstract: We present Gromov's celebrated reconstruction theorem in Lorentzian geometry. Based on that, we introduce several notions of convergence of (isomorphism classes of) normalized bounded Lorentzian metric measure spaces, for which we describe several fundamental properties. A modification of our reconstruction theorem also sheds new light into the spacetime reconstruction problem from quantum gravity. Partly in collaboration with Clemens Sämann (University of Vienna). Preprints are available at arXiv:2507.01907 (accepted at Classical and Quantum Gravity) and arXiv:2506.10852.
March 18, 2026, 11:30 am EST !!! (10:30 am Central !!!/16:30 pm Paris/11:30 pm Beijing)
Speaker: Mauricio Che (University of Vienna) Recording
Title: Gromov's compactness theorem for timed-metric spaces.
Abstract: In this talk, I will present recent joint work with Perales and Sormani (DOI: 10.1016/j.difgeo.2026.102364) regarding a version of the classical Gromov’s compactness theorem for intrinsic timed-Hausdorff convergence. This notion of convergence was introduced by Sakovich and Sormani and is designed for "timed-metric spaces"—metric spaces endowed with 1-Lipschitz functions. A key element of our proof is the formalization of an idea originally suggested by Gromov: describing Gromov–Hausdorff convergence via "addresses," which allows it to be treated as a form of uniform convergence.
April 01, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/11:30 pm Beijing)
Speaker: Albachiara Cogo (Scuola Normale Superiore di Pisa)
Title: Sobolev conformal structures on closed manifolds
Abstract: Low-regularity metrics arise naturally in the realm of geometric PDEs, especially in relation to physical models. It is well known in Riemannian geometry that the components of such metrics have the best regularity in harmonic coordinates. In this talk, we introduce a novel approach to globalize this idea and study conformal classes of rough Riemannian metrics on closed 3-manifolds. Given a Riemannian metric in the Sobolev class W^{2, q} with q > 3, we characterize when a more regular representative exists in its conformal class. We highlight a deep link to the Yamabe problem for rough metrics, which we fully resolve. In particular, for Yamabe positive metrics, the Yamabe problem in this low-regularity setting requires developing new elliptic theory for the conformal Laplacian, including existence, regularity and a fine blow-up analysis of its Green function, which we provide in any dimension n \geq 3 and for q>n/2. This is based on joint work with R. Avalos and A. Royo Abrego.
April 15, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/11:30 pm Beijing)
Speaker: Hunter Stufflebeam (Johns Hopkins University)
Abstract: TBD
April 29, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/11:30 pm Beijing)
Speaker: Argam Ohanyan (University of Toronto)
Abstract: TBD