Planned seminars

Europe/Lisbon —

Marcos Jardim

Marcos Jardim, Universidad Estadual de Campinas

We consider a class of geometric Bridgeland stability conditions for 3-folds of Picard rank one, parametrized by the upper half plane. We study the geometry of numerical walls, applying our results to prove that Gieseker semistability is equivalent to a strong form of asymptotic semistability along a class of paths in the upper half plane.
Finally, we compute all of the walls and describe the Bridgeland moduli spaces for the Chern character (2,0,-1,0) on complex projective 3-space in a suitable region of the upper half plane. Joint work with Antony Maciocia.

Europe/Lisbon —

Camilla Felisetti

Camilla Felisetti, Università di Trento
To be announced

Europe/Lisbon —

Alberto Abbondandolo

Alberto Abbondandolo, Ruhr Universität Bochum

The prototypical question in metric systolic geometry is to bound the length of a shortest closed geodesic on a closed Riemannian manifold by the volume of the manifold. This question has been extensively studied for non simply connected manifolds, but in the recent years there has been some progress also for simply connected manifolds, on which closed geodesics cannot be found simply by minimizing the length. This progress involves extending systolic questions to Reeb flows, a class of dynamical systems generalising geodesic flows. On the one hand, this extension and the use of symplectic techniques provide some answers to classical questions within metric systolic geometry. On the other hand, new questions arise from the more general setting and relate seemingly distant fields such as the study of rigidity properties of symplectomorphisms and the integral geometry of convex bodies. I will give a non-technical panoramic view of some of these recent developments.

Europe/Lisbon —

Carolina Araujo

Carolina Araujo, Instituto de Matemática Pura e Aplicada

Fano manifolds, i.e., complex projective manifolds having positive first Chern class, play a key role in higher dimensional algebraic geometry. The positivity condition on the first Chern class has far reaching geometric and arithmetic implications. For instance, Fano manifolds are covered by rational curves, and families of Fano manifolds over one dimensional bases always admit holomorphic sections. In recent years, there has been great effort towards defining suitable higher analogues of the Fano condition. Higher Fano manifolds are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional rational varieties, and families of higher Fano manifolds over higher dimensional bases should admit meromorphic sections (modulo Brauer obstruction). In this talk, I will discuss a possible notion of higher Fano manifolds in terms of positivity of higher Chern characters, and describe special geometric features of these manifolds.

Europe/Lisbon —

Antoine Song

Antoine Song, Princeton
To be announced

Europe/Lisbon —

Yael Karshon

Yael Karshon, University of Toronto

Together with Jihyeon Jessie Yang, we are resurrecting an old idea of Raoul Bott for using large torus actions to construct canonical bases for unitary representations of compact Lie groups. Our methods are complex analytic; we apply them to families of Bott-Samelson manifolds parametrized by C^n. Our construction requires the vanishing of higher cohomology of sheaves of holomorphic sections of certain line bundles over the total spaces of such families; this vanishing is conjectural, hence the question mark in the title.

Europe/Lisbon —

Olivia Dumitrescu

Olivia Dumitrescu, University of North Carolina at Chapel Hill
To be announced