Abstracts
Schedule:
Abstract:
Alejandro Cabrera:
Title: About non-formal quantization of Poisson brackets
Abstract: This will be an overview talk in which we shall discuss different approaches to quantization of Poisson brackets, with an emphasis on non-formal deformations. We shall first focus on highlighting some of the physical aspects behind these ideas and try to account for (at least part of) the corresponding wide range of ramifications in mathematics. Then, we will mention recent results in the non-formal context and their connection to Lie theory, including the relation to Kontsevich's formal quantization formula, the Poisson Sigma model, and the relation to the integrability by a symplectic groupoid (the latter is work in progress with R. Fernandes).
Rui Loja Fernandes
Title: Linear models and linearization problems around leaves
Abstract: I will survey several recent results, both published and unpublished, about local models and linearization around leaves for geometries which have an underlying real or complex Lie algebroid. I will focus mainly in the cases of general Lie algebroids, Poisson manifolds and generalized complex manifolds. This talk is based on joint work with Ioan Marcut (Koln) and my PhD student Sambit Senapati.
Thomas de Fraja
Title: Generalized ricci flow and spinors via Courant algebroid relations
Abstract: Using the theory of Courant algebroid relations already discussed, we first discuss a notion of related divergences and generalised ricci tensors. In the T-duality setting, we are able to transport the divergence, and hence the ricci tensor, to the T-dual manifold. We show that the generalised ricci flow is compatible with the T-duality relation R. Secondly, we explore how the space of spinors on related Courant algebroids are related, via irreducible representations of the Clifford algebra generated by R. As an application, we recover the well known isomorphism of twisted differential complexes.
Ideal Majtara
Title: Blowup formula for equivariant Donaldson invariants.
Abstract: TBA
Pavlo Gavrylenko
Title: Symplectic geometry of Isomonodromic tau functions on a torus
Abstract: TBA
Vincenzo Emilio Marotta
Title: Courant Algebroid Relations and T-duality
Abstract: Starting from the well-known notions of reduction of exact Courant algebroids over foliated manifolds and generalised isometry, the concept of transverse generalised isometry will be introduced and characterised. It will be shown how this leads to a definition of T-duality for exact Courant algebroids and an existence and uniqueness result for T-dual generalised metrics. Its main application to T-duality with a correspondence space will be discussed.
Ivan Penkov
Title: Linear embeddings of grassmannians and isotropic grassmannians.
Abstract: We call an embedding of grassmannians, one or both of them being isotropic, linear if it induces an
isomorphism on Picard groups. In this talk I plan to classify and describe explicitly all linear embeddings of grassmannians,
except when one of them is a spinor orthogonal grassmannian.
Roberto Rubio:
Title: Generalized geometric structures and invariants on 3-manifolds
Abstract: Complex and symplectic manifolds are, in particular, generalized complex manifolds, a class that supersedes them: there exist neither complex nor symplectic manifolds that are generalized complex. This happens very tightly, as generalized complex manifolds must be almost complex (and hence even dimensional). In this talk, I will show how Bn-generalized geometry, a simple and natural variation of generalized geometry, offers a similar setup for manifolds of any dimension and I will focus on the analogue of generalized complex structures for 3-manifolds and their associated invariants. This is joint work with J. Porti.
Jacopo Stoppa:
Title: Some applications of canonical metrics to Landau-Ginzburg models
Abstract: To a smooth del Pezzo surface or Fano threefold X, with a fixed Kähler class and a Gorenstein toric degeneration, toric mirror symmetry associates a compactified Landau-Ginzburg model, i.e. a type of fibration, such that some symplectic invariants of X can be computed from the complex geometry of the fibration. I will discuss the problem of constructing a corresponding map at the level of moduli spaces, from a domain U in the complexified Kähler cone of X to a well-defined, separated moduli space M of polarised manifolds. I will show a complete result for del Pezzos and a partial result for some special Fano threefolds. The construction uses transcendental methods, in particular some fundamental results in the theory of constant scalar curvature Kähler metrics. As a consequence M parametrises K-stable manifolds and U is endowed with the pullback of a Weil-Petersson metric.