Noticimat 3

Hora: 15:30 GMT-6

Enlace de transmisión: https://bluejeans.com/759804451

Ponente: Souvik Goswami (Universität Regensburg)

Título: Height pairing on higher cycles and mixed Hodge structures

Resumen: The height pairing between algebraic cycles over global fields is an important arithmetic invariant.  It can be written as sum of local contributions, one for each place of the ground field. Following Richard Hain, the Archimedean component of the height pairing can be interpreted in terms of an invariant of a certain mixed Hodge structure, called Biextension. 

In the paper https://doi.org/10.1016/j.aim.2019.02.003, we defined a height pairing for higher cycles as a consequence of arithmetic intersection theory of higher arithmetic cycles. In this talk we will explore the Archimedean contribution of this new height pairing and interpret it as an invariant associated to a mixed Hodge structure. 

This is joint work with J.I. Burgos Gil and G. Pearlstein (https://arxiv.org/abs/2007.06036). 

 

Hora: 19:45 GMT-6

Enlace de transmisión: https://cuaed-unam.zoom.us/j/96975648353

 

Ponente 1: Santiago Arenas Velilla (CIMAT)

Título: Transformada de sesgo para el número de cruces en árboles aleatorios

Resumen: El método de acoplamientos de sesgo de tamaño (Size-biased couplings) para el método de Stein es uno de los enfoques para demostrar teoremas límites en probabilidad cuando tenemos variables aleatorias no negativas y es especialmente útil para sumas de variables aleatorias no necesariamente independientes. Por otra parte, el número de cruces en árboles aleatorios uniformes con vértices en posición convexa cumple un teorema de límite central. En esta charla se muestra cómo es el uso de la transformada de sesgo de tamaño para obtener una prueba alternativa al resultado anterior, además de dar tasas de convergencia. Este es un trabajo conjunto con Octavio Arizmendi Echegaray.

Ponente 2: Larry Goldstein

Título: Ordenación y la aproximación de Dickman para el algoritmo Quickselect

Resumen: Descarga en https://tinyurl.com/y5f62wlj

 

Hora: 12:00 GMT-6

Enlace de transmisión: https://youtu.be/Nzk-48zr1nA

Ponente: Christoph Benzmüller (FU Berlin & Latentine GmbH)

Título: Classical higher-order logic. Automation and selected applications

Resumen: Automated theorem proving (ATP) and interactive theorem proving (ITP) in higher-order logic (HOL) has made significant progress over the past decades. Powerful HOL-ATP systems are available today that can solve non-trivial problems automatically. Moreover, ATP systems for propositional and first-order logic have been successfully integrated with modern ITP systems such as Isabelle, HOL-light, Coq, Lean, and others, and these integrations are key for future applications beyond the academic context. Together with colleagues and students I have been contributing to this challenge area for more than 25 years. Research output includes, among others, the Leo-family of ATP systems for HOL, the development of an associated, international HOL-ATP infrastructure (TPTP THF), and foundational work on the semantics and proof theory of HOL. In the first part of my presentation I will outline these contributions to the automation of HOL.

Since about a decade I have also pioneered, in collaboration with others, an orthogonal research direction: he automation of expressive non-classical logics (NCLs), which have prominent applications in AI, computer science, philosophy, mathematics, natural language processing. My research hypothesis has been that expressive NCLs and their combinations can easily be mechanised by semantically embedding them (in a shallow way) as object logics in HOL. HOL thereby serves as a meta-logical framework in which expressive NCLs and their combinations can be encoded and automated. In the second part of my talk I will outline the universal meta-logical reasoning approach and sketch some successful recent applications

 

Hora: 10:00 GMT-6

Enlace de transmisión: meet.google.com/dgx-ovge-npc

Ponente: Dr. Chayan Adelki de la Cruz Reyes (CIMAT)

Título: Caracterización de los operadores firmemente no expansivos invariantes bajo renormamientos

Resumen: La propiedad de punto fijo no se preserva bajo renormamientos equivalentes, ya que al renormar a un espacio de Banach cambia su estructura algebraica y geométrica. Más aún, dadas dos normas no colineales, los conjuntos de operadores no expansivos con respecto a las dos normas son diferentes. En esta charla se caracterizará a los operadores firmemente no expansivos (FNE), en el caso real y complejo, que son invariantes bajo renormamientos equivalentes, los cuales son una subfamilia de los operadores no expansivos.  

Felicitamos a Ulises Rodríguez Domínguez, quien este viernes obtuvo el grado de Doctor en Ciencias con Orientación en Ciencias de la Computación con la defensa de la tesis Regularized Dictionary Based Methods For Pattern Recognition In Images. En el jurado participaron el Dr. Jean Bernard Hayet (CIMAT), presidente; el Dr. Julio César Estrada Rico (CIMAT), secretario; el Dr. Rogelio Ramos Quiroga (CIMAT), vocal; el Dr. Hugo Jair Escalante Balderas (INAOEP), vocal; y el Dr. Óscar Susano Dalmau Cedeño (CIMAT), vocal y director de la tesis.

Divulgación