Seminários
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Curvature homogeneous hypersurfaces
Seminário de Geometria Diferencial
Exposer: Luis Florit
Institution: IMPA
Local: SALA 236
Summary:
We provide a classification of all curvature homogeneous hypersurfaces in space forms. Besides the obvious cases and a single example in $H^5$ discovered in the 80's, that we recover, the only case left was completely open: the 3-dimensional one in both $S^4$ and $H^4$. We show that, in each of these two space forms, there is a one parameter family of hypersurfaces without symmetries, and a single algebraic example with a circle of symmetries. Moreover, these are essentially all of them.
This is a joint work with Robert Bryant and Wolfgang Ziller.
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Neural Conjugate Flows: Physics-Informed Architectures with Differentiable Flow Structure
Seminário de Computação Gráfica
Exposer: Arthur Bizzi
Institution: IMPA
Local: AUDITORIO 3
Summary:
We present Neural Conjugate Flows, a novel design for physics-informed neural networks with flow structure. We prove that this architecture is an universal approximator for solutions of differential equations and demonstrate how its group and topological lead to computational and theoretical gains when simulating dynamical systems with neural networks.
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Data Science and Innovation
Palestra Especial
Exposer: Patrick Valduriez
Institution: Inria, France
Local: AUDITORIO 1
Summary:
Data science and innovation have become overloaded terms, leading to some confusion. To be successful, the innovation process involves not only inventions (e.g., new methods) but also context, e.g., user behavior and timing, e.g., market readiness. In this talk, I discuss the impact of data science on innovation, using selected success stories (some of which I was involved in). I also give hints to promote innovation within companies, in particular, using open innovation. Finally, I describe some innovations in the context of the Inria-Brasil partnership.
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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.