Iniciativa de los/las alumnos/as del Programa en Consorcio de Doctorado en Matemática, impartido conjuntamente por la PUCV, UTFSM y la UV.

Únete como espectador/a o expositor/a en este seminario de postgrado en matemática organizado por estudiantes de doctorado.

Dependiendo del día se utilizará una distinta sala de reunión para el seminario; aquí se incluyen las ubicaciones correspondientes:

18/06 (La charla será en español)

Título: From PINNs to RVPINNs.

Resumen: In recent years, machine learning has gained recognition as an effective method for approximating solutions to partial differential equations (PDEs). This approach involves training neural networks using both data and numerical constraints. Physics-Informed Neural Networks (PINNs) incorporate the strong form of the PDE into the loss function, allowing the network to learn the solution by minimizing the residual. Variational Physics-Informed Neural Networks (VPINNs) extend this idea through a Petrov–Galerkin framework, embedding the variational form into the loss, where the trial space is represented by a neural network and the test space is finite-dimensional. More recently, Robust VPINNs (RVPINNs) have been introduced to enhance stability and robustness by minimizing a discrete dual norm of the residual.

In this talk, we will review the evolution from PINNs to RVPINNs, highlighting their key ideas. A challenge in RVPINNs is the need to invert a Gram matrix, which can become computationally expensive if the variational formulation and test space are not carefully designed. To address this, we propose a hybrid variational formulation that preserves the robustness of RVPINNs while significantly reducing the computational cost.

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09/05

Título: Enumerative geometry using motivic theory

Resumen: When computing enumerative invariants on algebraic surfaces, one often has to work over an algebraically closed field. We will use an example to highlight the problems on other fields and how the motivic theory is a way to go around it.

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30/04

Título: An introduction to the generalized doubling method: the local case.

Resumen: In the global case, the classical doubling method of Piatetski-Shapiro and Rallis produced an integral representation for the standard L-function of an irreducible cuspidal automorphic representation of a classical group twisted by a grössencharacter. More recently, Cai, Friedberg, Ginzburg and Kaplan extended the construction to include twists by arbitrary cuspidal representations of GL_k, for all k. 

Bryan Pichucho (UTFSM), Henry Echeverría (UV), y Enzo Giannotta (PUCV). Estudiantes del doctorado en matemática.