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/10:30 pm Beijing)
Speaker: Albachiara Cogo (Scuola Normale Superiore di Pisa) Recording
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/10:30 pm Beijing)
Speaker: Hunter Stufflebeam (Johns Hopkins University)
Title: Almost Rigidity and the Volume Spectrum
Abstract: In the 1990’s, researchers such as Colding and Petersen investigated the stability of invariants such as the radius, volume, and Laplace eigenvalues λk of closed Riemannian manifolds with Ric≥(n-1)g. They showed that almost maximality of either the radius or volume, or minimality of λn+1 (listed with multiplicity), is equivalent to the closeness of the manifold of interest to the unit round sphere.
We contribute another invariant to this list in dimension n=3, by studying the almost-rigid properties of the first Almgren-Pitts width ω1 as a non-linear, minimal-surface-based analogue of Petersen's work with the Laplace eigenvalues λk.
April 29, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/10:30 pm Beijing)
Speaker: Argam Ohanyan (University of Toronto) Recording
Title: Timelike conjugate points in Lorentzian length spaces.
Abstract: Motivated by the work of Shankar-Sormani in metric length spaces, we introduce and study various notions of conjugate points along timelike geodesics in Lorentzian (pre-)length spaces, all of which equivalently characterize the classical notion defined via Jacobi fields in the setting of smooth, strongly causal spacetimes. Given the lack of a natural arclength parametrization compatible with a topological distance, we instead make use of the Fréchet distance to measure distances between timelike geodesics. We give two main applications of our notions: A timelike Rauch comparison theorem, as well as a result adjacent to the recently established Lorentzian Cartan-Hadamard theorem of Erös-Gieger. This talk is based on the arxiv preprint 2509.12855, which is joint work together with James D.E. Grant (U. Surrey), Michael Kunzinger (U. Vienna), Yasmin Schinnerl (previously U. Vienna), and Roland Steinbauer (U. Vienna).
May 13, 2026, 10:30 am EST (9:30 am Central/16:30 pm Paris/10:30 pm Beijing)
Speaker: Chenkai Song (Nankai University)
Title: A Product Formula for Family Indices and Family Band Width Estimates
Abstract: Manifolds of positive scalar curvature (PSC) have long been an important topic in differential geometry. In 2018, Gromov conjectured a sharp upper bound on the width of PSC bands whose cross sections admit no PSC metric. In this talk, I discuss a family version of this problem for fiber bundles. After recalling some index-theoretic results of the original bandwidth conjecture, I will show that the family version holds for fiber bundles with infinite family A-hat area. One technical lemma in the proof is a product formula for family indices.