29/09/2020, 17:00 — 18:00 Europe/Lisbon —
Gonçalo Oliveira, Universidade Federal Fluminense, Brasil
$G_2$-monopoles (a summary)
This talk is aimed at reviewing what is known about $G_2$-monopoles and motivate their study. After this, I will mention some recent results obtained in collaboration with Ákos Nagy and Daniel Fadel which investigate the asymptotic behavior of $G_2$-monopoles. Time permitting, I will mention a few possible future directions regarding the use of monopoles in $G_2$-geometry.
06/10/2020, 17:00 — 18:00 Europe/Lisbon —
Éveline Legendre, Université Paul Sabatier
Localizing the Donaldson-Futaki invariant
We will see how to represent the Donaldson-Futaki invariant as an intersection of equivariant closed forms. We will use it to express this invariant as the intersection on some specific subvarieties of the central fibre of the test configuration. As an application we provide a proof that for Kähler orbifolds the Donaldson-Futaki invariant is the Futaki invariant of the central fiber.
13/10/2020, 17:00 — 18:00 Europe/Lisbon —
Xiuxiong Chen, Stony Brook University
On the space of Kähler metrics
Inspired by the celebrated $C^0, C^2$ and $C^3$ a priori estimate of Calabi, Yau and others on Kähler Einstein metrics, we will present an expository report of a priori estimates on the constant scalar curvature Kähler metrics. With this estimate, we prove the Donaldson conjecture on geodesic stability and the properness conjecture on Mabuchi energy functional.
This is a joint work with Cheng JingRui.
10/11/2020, 17:00 — 18:00 Europe/Lisbon —
Ana Rita Pires, University of Edinburgh
Many more infinite staircases in symplectic embedding functions
17/11/2020, 17:00 — 18:00 Europe/Lisbon —
Silvia Anjos, Instituto Superior Técnico and CAMGSD
Stability of the symplectomorphism group of rational surfaces