Mon, 23 Nov 2026
16:30 -
17:30
L4
Mon, 18 Jan 2027
14:15
14:15
L4
Mon, 30 Nov 2026
16:30 -
17:30
L4
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
16:00 -
17:00
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.
Thu, 29 Oct 2026
16:00
16:00
L4
Rational points of bounded height on surfaces
Tim Santens
(University of Cambridge (DPMMS))
Abstract
Manin and his collaborators initiated a program in 1989 with the goal of understanding the distribution of rational points of bounded height on Fano varieties, using methods from algebraic geometry and analytic number theory. Since then, there has been substantial progress on this program, including the formulation of a precise conjecture. I will discuss the achievements of this program since then, with a focus on surfaces, including some of my own work on quintic del Pezzo surfaces.
Mon, 09 Nov 2026
16:30 -
17:30
L4
The fast dynamo conjecture
Michele Coti-Zelati
(Imperial College )
Abstract
The fast dynamo conjecture, posed by Zeldovich and Sakharov and later recorded in Arnold’s book of problems, asks whether a smooth, autonomous, divergence-free flow on the three-torus can amplify magnetic fields exponentially at a rate bounded uniformly away from zero as the magnetic resistivity vanishes. In this talk, we resolve the conjecture by constructing a flow based on the classical stretch–fold–shear (SFS) mechanism. The proof uses anisotropic Banach spaces adapted to the ideal dynamics to obtain an isolated unstable eigenmode with a distributional eigenfunction. A singular spectral perturbation argument then shows that this instability persists for small positive resistivity. The construction is robust and yields an open set of smooth autonomous fast dynamos.
Mon, 02 Nov 2026
16:30 -
17:30
L4
Convergence of a vector-valued Allen-Cahn system to Brakke’s multiphase mean curvature flow
Tim Laux
(Heidelberg University)
Abstract
Allen-Cahn equations are popular phenomenological models for phase transitions that describe materials on a mesoscopic scale. The macroscopic scale observed by us humans corresponds to a singular scaling limit, the so-called sharp-interface limit, in which transition layers collapse onto hypersurfaces. Since Ilmanen’s pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand this sharp-interface limit of systems of coupled Allen-Cahn equations. In this talk, I will present the first global, unconditional convergence result for such a coupled system and show that the limit is a multiphase mean curvature flow in the sense of Brakke.
This is joint work with Keisuke Takasao (Kyoto University).