Seminários

Clifford structures and constant extrinsic curvature surfaces

Resumo: Constant extrinsic curvature surfaces in space forms are best understood as Sasakian objects living in the unitary bundle. In this framework they become bilegendrian surfaces. We discuss the insights this perspective provides on the study of constant extrinsic curvature surfaces.

Category Theory applied to Data Visualization

Resumo: Category Theory (CT) is a branch of mathematics that studies general abstract structures through their relationships, and it is unmatched in its ability to organize and relate abstractions. In recent years, CT has found applications in a wide range of disciplines, such as chemistry, biology, natural language processing, and database theory. We present a novel application by formalizing Data Visualization within Category Theory. This formalization creates a bridge between Mathematics and Data Visualizations. Moreover, it provides a framework to express complex visualizations, which can be implemented computationally by leveraging the well-established connection between CT and Functional Programming.

Fluxos assintoticamente seccionais hiperbolicos

Resumo: Recordamos a teoria de fluxos com singularidades e mostramos avanços no caso assintotico

Spectral data for Higgs bundles, an introduction

Resumo: The moduli space of Higgs bundles on a Riemann surface can be studied via a fibration over a vector space, with the generic fibre being an abelian variety. Designed with students in mind, our aim is to provide an informal introduction to Higgs bundles and the process of abelianization. If time allows, we will also touch upon nonabelianization techniques for Higgs bundles and elucidate how these concepts intersect with mirror symmetry.

Automorphic Green's functions on spin Shimura varieties and Kummer periods

Resumo: Motivated by the conjectures of Birch-Swinnerton-Dyer and Beilinson-Bloch, I will explain how to construct automorphic Green's functions on spin Shimura varieties, and how we expect these to be linked to motivic cohomology classes. This is based partly on joint work with Spencer Bloch.

This seminar will be in hybrid format. For the online access use the link: meet.google.com/hzq-vads-ntx

Free boundary minimal and CMC annuli in space forms

Resumo: We construct non-rotational, embedded CMC annuli with free boundary in the unit ball of $\mathbb{R}^3$, giving a negative answer to a question posed by Wente in 1995. These examples constitute the first annular solutions to the partitioning problem in the Euclidean ball that are not rotational. Moreover, we extend this result by constructing examples of free boundary minimal and CMC annuli in geodesic balls of the space forms $\mathbb{S}^3$ and $\mathbb{H}^3$. This is a joint work with Isabel Fernández and Pablo Mira.