Abstract: In this talk, we will see how to build Young structures for a broad family of partially hyperbolic systems, specifically those with a splitting into center-stable and strongly unstable directions. These are the same systems where Bonatti and Viana previously proved the existence of SRB measures. By adapting and refining existing techniques, we bring powerful statistical tools, like decay of correlations, the Central Limit Theorem, and large deviations, into a setting where they hadn’t been fully explored.

Abstract: In regression models, testing for goodness-of-fit corresponds to check if the hypothesized relationship between the response variable and the covariates adequately describes the observed data. However, some well-established tests are locally sensitive to model estimation errors. This requires computationally challenging bootstrap procedures where the model needs to be iteratively re-estimated. Focusing on generalized partially linear models, we design a simulation study to contrast the size and power of a class of tests under different null and alternative hypotheses, and different conditional moment restrictions. Also, supported by recent developments that consider Cramér-von-Mises-type test statistics based on Neyman-orthogonal kernels integrated via Gaussian processes, we propose a fast-bootstrap approach that can outperform existent methodologies.

Abstract: In this work we introduce a notion of tensor product of (twisted) quiver representations with relations in the category of O_X-modules. As a first application of our notion, we see that tensor products of polystable quiver bundles are polystable and later we use this to both deduce a quiver version of the Segre embedding and to identify distinguished closed subschemes of GL_n(C)-character varieties of free abelian groups.

Abstract:  Higgs bundles and their moduli space are an increasingly central objects in modern geometry, lying at the intersection of several of its branches. In this talk, we aim to give an accessible introduction to these objects and their relation with theoretical physics, namely the phenomenon of mirror symmetry. This can be better understood by looking at special subvarieties of the moduli space called Lagrangians. If time allows, we will describe a novel way to produce such Lagrangians.