Register here:
All talks will take place on 3 December 2025!
9.00 Welcome
9.15 Dan Disney
10.15 Coffee Break
10.40 Vanessa Ryborz
11.45 Emanuele Caputo
12.45 Lunch
14.00 Darya Sukhorebska
15.00 Coffee Break
15.30 Raquel Perales
16:30 End
Sub-Riemannian Structures on Exotic 7-Spheres
Sub-Riemannian structures of high codimension (greater than one) are rare on 7-manifolds. Until recently, only three such examples were known on any of the homotopy 7-spheres: two on the standard 7-sphere and one on the Gromoll–Meyer exotic sphere. In this talk I will describe new examples of step-2, codimension-3 sub-Riemannian structures on every homotopy (exotic) 7-sphere.
Infinitesimal Hilbertianity for Riemannian manifolds with metrics of low regularity
Various concepts from smooth differential geometry allow generalisations to metric measure spaces. This includes a generalised first order calculus leading to a synthetic definition of the Sobolev space W^{1,2}. A metric measure space is called infinitesimally Hilbertian if the associated Sobolev space W^{1,2} is a Hilbert space. A vast class of metric measure spaces arises from manifolds equipped with non-smooth Riemannian metrics.
In this talk, we compare the classical differential calculus on manifolds with the synthetic first order calculus on metric measure spaces in the setting of a manifold M endowed with a low regularity Riemannian metric g. We then study under which regularity assumptions on g the induced metric measure space is infinitesimally Hilbertian.
Recent progress on the structure of metric 1-currents
The goal of the talk is to give an overview of the metric theory of currents by Ambrosio-Kirchheim, together with some recent progress. Metric currents are a generalization to the metric setting of classical currents. Classical currents are the natural generalization of oriented submanifolds, as distributions play the same role for functions. We present a structure result for metric 1-currents as superposition of 1-rectifiable sets in complete and separable metric spaces, which generalizes a previous result by Schioppa. This is based on an approximation result of metric 1-currents with normal 1-currents and a more refined analysis in the Banach space setting. This is joint work with D. Bate, J. Takáč, P. Valentine, and P. Wald (Warwick).
Positively curved manifolds with low symmetry rank
We study simply connected, even-dimensional manifolds with positive curvature that admit an effective isometric torus action. If the dimension of the torus is large enough, one can recover the topological invariants of the manifold. We will discuss the classical results on this topic and present the recent developments. In particular, we will show that the Euler characteristic of the 16-dimensional manifolds with 3-dimensional torus action coincides with one of the 16-dimensional rank one symmetric spaces. Moreover, all isotropy representations of the corresponding Z_2^3-subactions coincide. This result is joint work with Burkhard Wilking.
A Compactness Theorem for the Intrinsic Timed-Hausdorff Distance
The intrinsic timed-Hausdorff distance between timed-metric-spaces was first defined by Sakovich-Sormani to define a weak notion of convergence for space-times. In this talk, I will present a compactness theorem for the Intrinsic timed Hausdorff convergence of timed-metric spaces. This proof uses timed-Fréchet maps as isometric embeddings. (Joint work with M Che and C Sormani).
The talks will take place in Cardiff University's Abacws Building room 3.38.
The closest train station is Cathays, which is 6 minutes by train from Cardiff Central, and 30 minutes away by foot.
The Cardiff University stop for National Express buses is also very convenient.
The talks will take place in Room 3.38 at Abacws Building.
The coffee breaks will take place in the common room on the same floor.