Seminários
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A complete solution to Lamé equations with finite monodromy
Seminário de Geometry, Arithmetic and Differential Equations of Periods (GADEPs)
Exposer: Chin-Lung Wang
Institution: NTU, Taiwan
Local: Palestra Virtual / Online Lecture
Summary:
It is a well known result of Beukers and Walll that the classical Lamé equation on a torus w'' = (n(n + 1) P(z) + B)w has finite monodromy only if the parameter n belongs to a finite set of rational numbers mod 1. By combining geometry of spherical tori with combinatorics of dessins d'enfants, we give an exact counting formula for every such n and monodromy group M, and describe the construction of each Lamé equation. This is a joint work with You-Cheng Chou and Po-Sheng Wu. The reference is arXiv:2402.16286. Online talk: meet.google.com/hzq-vads-ntx
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Automorphic forms for triangle groups: properties of integrality of coefficients
Colóquio dos Alunos
Exposer: Frederico Bianchini
Institution: IMPA
Local: SALA 224
Summary:
Modular forms have interesting connections with the counting of geometric objects (e.g., the Modularity Theorem), and the integrality properties of coefficients of certain modular forms play a fundamental role in this. An exposition will be given on an article by H. Movasati and Khosro M. Shokri published in 2014, which deals with integrality properties of modular forms for triangular groups. The goal of the presentation is to introduce the audience to related topics, with the article and its results as a backdrop.
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Clifford structures and constant extrinsic curvature surfaces
Seminário de Geometria Diferencial
Exposer: Graham Smith
Institution: PUC-Rio
Local: SALA 236
Summary:
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.
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Category Theory applied to Data Visualization
Seminário de Computação Gráfica
Exposer: Davi Sales Barreira
Institution: Fundação Getúlio Vargas - EMAp
Local: AUDITORIO 3
Summary:
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.
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Free boundary minimal and CMC annuli in space forms
Seminário de Geometria Diferencial
Exposer: Alberto Cerezo
Institution: Universidad de Granada
Local: SALA 236
Summary:
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.