Mon, 12 Oct 2026
14:15
14:15
L4
Cayley fibrations have singular fibres
Jacek Rzemieniecki
(HU Berlin)
Abstract
Calibrated fibrations are expected to play an important role in exceptional holonomy, much as special Lagrangian fibrations do in the SYZ picture for Calabi--Yau manifolds. Singular fibres are expected to be essential, and a natural question is whether they are forced by the geometry. In his PhD thesis, Baraglia showed that coassociative fibrations of compact full-holonomy G_2-manifolds must have singular fibres. The analogous problem for Cayley fibrations remained open for many years and turns out to be substantially more difficult, with its resolution relying on deep results from 4-manifold topology.
The proof takes some unexpected twists and turns, involving a Diophantine equation arising from the Spin(7)-structure, families Seiberg--Witten theory and parametrized homotopy theory. After a short crash course on Spin(7) geometry, I will explain how these pieces fit together. This is joint work with Jianfeng Lin and Viktor Majewski.
Mon, 19 Oct 2026
16:30 -
17:30
L4
A structure theorem for properly embedded CMC surfaces and applications
Giuseppe Tinaglia
(Kings College London)
Abstract
I will discuss the geometry of genus zero CMC surfaces embedded in Euclidean space and, among other things, prove a local area estimate for such surfaces. This is joint work with Bill Meeks.
Mon, 09 Nov 2026
16:30 -
17:30
L4
Mon, 12 Oct 2026
16:30 -
17:30
L4
Regularity of oblique transmission problems
Iñigo Urtiaga Erneta
(Universitat Politecnica de Catalunya)
Abstract
Transmission problems model phenomena in domains composed of several adjacent phases. While a variational ''divergence-form'' theory is by now classical, a non-variational framework has only emerged more recently. This talk concerns the regularity of viscosity solutions to such transmission problems in non-divergence form.
I will present new regularity results in the case of flat interfaces, where the transmission condition may depend on both the normal and tangential derivatives of the solution. This condition can be viewed as a nonlinear coupling of oblique derivatives across the interface. Our main result establishes optimal piecewise $C^{1,\alpha}$ regularity for viscosity solutions.