Speaker: Esther Cabezas-Rivas

Title: "Ricciflowing" space-time (or how to construct Canonical Ricci Solitons)

Abstract: In this talk, we will describe how the theory of optimal transport can lead to new Ricci flow results independent of optimal transport itself. In particular, given a Ricci flow on a manifold M  over a time interval I, we introduce a second time parameter, and define  natural gradient Ricci solitons on the space-time M \times I.

As an application, we shall see how our construction encodes various of the monotonic quantities that underpin

Perelman's work on Ricci flow, and how the different Harnack inequalities (and also new ones) naturally arise as simple curvature conditions on the space-time solitons.

Speaker: Teresa Arias-Marco

Title: Symmetric-like Riemannian manifolds and their relation with the spectrum of the Laplace operator.

Abstract: D’Atri spaces, manifolds of type A, probabilistic commutative spaces, C-spaces, TC-spaces, and GC-spaces have been studied by many authors as symmetric-like Riemannian manifolds. Another class of interest is the class of weakly symmetric manifolds however, we consider the local version of this property throughout our work. During the talk we will show open problems relative with the previous kind of manifolds and we will answer the following question: Are the previous properties on closed manifolds determined from the eigenvalue spectrum of the associated Laplace operator on functions?

Joint work with Dorothee Schueth.

Speaker: Fernando Galaz

Title: Nonnegatively curved manifolds with large isometric group actions.

Abstract: The study of Riemannian manifolds with nonnegative (sectional) curvature has

remained an area of active research in which metric aspects of differential geometry,

such as comparison arguments, play a central role. In this context, considering manifolds with a “large” isometric group action provides

a systematic approach to the study of both positively and nonnegatively curved manifolds. I will present different interpretations of a "large" isometric action and,  as an illustration, I will discuss the classification in low dimensions of nonnegatively curved Riemannian manifolds with a fixed-point homogeneous isometric Lie group action.

Speaker: Oscar Macia

Tittle: SO(3)-STRUCTURES ON AQH 8-MANIFOLDS

Abstract: We will review aspects of Quaternionic Kähler (QK) geometry and the geometry of Almost Quaternionic Hermitian (AQH) manifolds from the point of view of G-structures and Gray--Hervella classes. For the 8 dimensional case the study of the intrinsic torsion of SO(3)-structures factoring through

Sp(2)Sp(1) will lead to an example of a nearly quaternionic structure on SU(3): a non-QK AQH 8-manifolds for which the three Kähler 2-forms span a differential ideal.

Speaker: Farid Madani

Title:  Equivariant Yamabe problem and Hebey-Vaugon conjecture.

Abstract: In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this lecture, I introduce the equivariant Yamabe problem for compact Riemannian manifolds and explain how Hebey-Vaugon conjecture solves this problem, and give some recent results about this conjecture.

Speaker: Esther Vergara

Title: *Harmonic Geometric Structures*

Abstract: Parting from the definition of harmonic maps, we motivate, using vector fields as maps between smooth manifolds, why a generalization of the concept of harmonicity is needed for section between bundles. We will show how the sections of the homogeneous twistor bundle are associated with geometric structures, and defined harmonic geometric structures as the geometric structures with associated harmonic section and not the associated section of the twistor bundle are given.  (Almost complex structures, almost contact structures and $f$-structures.)  Application to submersions between K-contact structures and (1,2)-symplectic manifolds,  warped products of almost hermitian structures with the real numbers and hypersurfaces of almost hermitian structures are studied in terms of their harmonicity. 

Speaker: Mario Micallef

Title: Constant mean curvature surfaces with prescribed ideal boundary in negatively curved 3-manifolds.

Abstract: I shall describe some existence/nonexistence theorems for constant mean curvature disks and annuli with boundary on the sphere at infinity in hyperbolic 3-space. I shall outline some work of my student Thomas Cuschieri on the continuous dependence of constant mean curvature disks on their ideal boundary. The relation of stability of constant mean curvature surfaces to Yau's isoperimetric inequality in a negatively curved 3-manifold will also be discussed.