Winter Meeting on Geometry and Physics UASLP 2022

FEBRUARY 31 and March 1, 2022

FACULTAD DE CIENCIAS, UASLP (CAMPUS PEDREGAL)


A 2-day meeting dedicated to geometric and physical
aspects of quantization, mathematical modeling, quantum
field teory and general relativity, among others.


Winter Meeting on Geometry and Physics

UASLP 2022

We are very glad to invite you to the 2020 edition of our annual Winter Meeting on Geometry and Physics, to be hold from Wednesday 26 to Friday 28, February, 2020, in the City of San Luis Potosi.

In this occasion, the meeting will be dedicated to mathematical and physical aspects of geometric structures present in modern theoretical physics,  ranging over a variety of  topics  including , classical field theories, gauge symmetries, mathematical modeling , quantum field theory and general relativity, among others.

The three days meeting aims to bring together the national community interested in topics of geometric aspects of quantization and related subjects, in order to discuss recent results, to interchange ideas, to present our current projects and to spend a good time with colleagues and students.  

The  Winter Meeting on Geometry and Physics UASLP 2020 will include a couple of mini courses, some invited plenary talks and we will include several short talks based on the demand.  

The meeting will be held in both english and spanish

There is no registration fee

Mini Courses

The WMGP-UASLP 2020 will be held at the Auditorio,  Edificio 1, Facultad de Ciencias UASLP, Campus Pedregal. The Python course will be held at the Laboratorio de Matemática Educativa, Edificio 1.

Héctor Hugo García Compean
Cinvestav

Introducción a la Teoría Conforme de Campos en 2d
 
 En este curso daremos una introducción a las teorías cuánticas de campos conformes en dos dimensiones. Introduciremos nociones
básicas de la teoría y daremos algunos ejemplos explícitos. Se estudiarán también  representaciones del álgebra de Virasoro. Consideraremos el caso más general cuando aparte de la simetría conforme se tienen simetrías globales  no-Abelianas, con campos tomando valores en el álgebra del Lie.  Finalmente, si el tiempo lo permite, estudiaremos la teoría sobre el toro.

Jesús Madrigal Melchor
LUMAT-UAZ

Introducción a python para cálculo científico

En este mini-curso se hará un recorrido por los elemento básicos de python como lenguaje de programación usado para cálculo científico. En la primera parte del curso (primer día) se instalará el ambiente de trabajo anaconda python 3.7, así como los elemento básicos de un lenguaje de programación como son variables, entrada y salida, funciones, condicionales y ciclos, entre otras elementos. Para la segunda parte (segundo y tercer día) se mostrará un panorama general de como python se puede usar para resolver problemas en la física. Programa

Tatjana Vukasinac
(UMSNH)

Análisis canónico de teorías de norma en presencia de fronteras

En este mini-curso vamos a analizar la descripción canónica de teorías de norma, empezando con el formalismo de Dirac y de su modificación introducida por Regge y Teitelboim para tratar teorías definidas en las regiones con frontera. También, presentaremos un repaso del análisis Hamiltoniano usando las herramientas de geometría simpléctica. Vamos a mostrar que en algunos casos, cuando la estructura simpléctica del sistema tiene términos de frontera, el formalismo de Dirac-Regge-Teitelboim (DRT) necesita una extensión que permite la descripción canónica consistente. Para ilustrar estas ideas vamos a estudiar dos ejemplos. En el primer ejemplo vamos a comparar dos teorías: Maxwell + U(1) Pontryagin, con Maxwell + U(1) Chern-Simons, donde las teorías de Maxwell y Pontryagin están definidas en un espacio-tiempo con frontera y la teoría de Chern-Simons está definida en la frontera. Estos dos sistemas tienen una descripción Lagrangiana equivalente, pero sus descripciones canónicas difieren, en el primer caso la estructura simpléctica no tiene términos de frontera, mientras que en el segundo caso sí los tiene y se necesita usar la extensión del método de DRT. Vamos a mostrar cómo se relacionan estas diferentes descripciones. Como un segundo ejemplo vamos a analizar la teoría de gravedad en el formalismo de primer orden, en presencia de un horizonte aislado. En este caso la estructura simpléctica tiene una contribución en el horizonte que es necesaria para la descripción consistente de la teoría dentro del formalismo canónico. 

Plenary Talks

Yuri Bonder 
(ICN-UNAM)

Filed theories with nondynamical fields

I will first present a formalism to study symmetries in the context of diffeomorphism-invariant gauge theories. With it, I will show a universal symmetry algebra that contains the gauge symmetry and a covariant version of the diffeomorphisms. Then, I will include nondynamical fields that are supposed to describe effects associated with more fundamental degrees of freedom. Typically, these objects reduce/break the symmetries of the theory, and I will present a method to find the residual symmetries. I will present some results obtained with this method in theories with explicit Lorentz invariance and for the Unimodular Theory of Gravity, which is only invariant under a subgroup of diffeomorphisms.

Miguel Ángel García Ariza
(ASU-Qro)

Geometric structures induced by physics

The possibility to describe the states of a physical system with a privileged set of coordinates endows the corresponding configuration space with a geometric structure. In this talk, I shall present some particular examples of how this occurs. I will also illustrate how this relationship between physics and geometry allows for a coordinate-free approach to concepts whose definition usually resorts to coordinates, such as "extensive functions".

Sujoy Modak
(FC-UCol)

New geometric and quantum field theoretic aspects of the radiation dominated early universe

I shall show that upon a conformal transformation, the usual FRW metric in cosmological frame (and defined in the radiation dominated phase), can be transformed into a spherically symmetric form which allows several interesting features. These features can be broadly divided into geometric and field theoretic parts. On the geometric side the new coordinates allow: (i) to introduce observer dependent horizons, (ii) a new foliation of spacetime in terms of ''time'' and ''space'' slices; on the other hand on the quantum field theory side we find: (i) a new, unitarily inequivalent quantization for massless scalar fields, (ii) a new and well defined vacuum state (which we refer as the T-vacuum). This in turn lead us to (iii) a nonzero particle number density for cosmological observers in the T-vacuum, and (iv) well-defined expressions of renormalized energy-momentum tensor in the cosmological as well as comoving frames which then justify the validity of the T-vacuum state. I shall also present a side by side comparison of this process with Unruh effect and comment on the importance of this discovery.

Miguel Sabido
(UGto)

TBA

Mariano Celada
(CCM-UNAM)

Escaping second-class constraints in general relativity

In this talk we perform the canonical analysis of first-order general relativity in all dimensions and show that it is possible to completely avoid the introduction of second-class constraints during the entire process while manifestly preserving the gauge invariance of the theory under the n-dimensional Lorentz group.

Ángel Manuel Rodríguez López
(UASLP)

Covariant momentum map for non-Abelian BF theory

In this talk, we analyze the inherent symmetries associated to the non-Abelian topological BF theory from the geometric and covariant perspectives of the Lagrangian and the multisymplectic formalisms. At the Lagrangian level, we classify the symmetries of the theory as natural and Noether symmetries and construct the associated Noether currents, while at the multisymplectic level the symmetries of the theory arise as covariant canonical transformations. These transformations allowed us to build within the multisymplectic approach, in a complete covariant way, the momentum maps which are analogous to the conserved Noether currents. The covariant momentum maps are fundamental to recover, after the space plus time decomposition of the background manifold, not only the extended Hamiltonian of the BF theory but also the generators of the gauge transformations which arise in the instantaneous Dirac-Hamiltonian analysis of the first-class constraint structure that characterizes this topological field theory. So, this study shed some light on the understanding of the manner in which the generators of gauge transformations may be recovered from the multisymplectic formalism for classical field theory. 

Short talks

Efrain Ruiz Alvarado
(BUAP)

Torsores y Espacios Homogéneos

Usualmente en la física tenemos cantidades de las cuales sólo podemos medir la diferencia, generalmente esto es debido a la libertad para escoger un origen desde el cual vamos a medir. En esta charla se da una definición de la estructura que surge en estos sistemas en donde sólo podemos tomar diferencias o proporciones, llamada Torsor, la cual viene además con un grupo, se dan ejemplos de ellos en Termodinámica, Electromagnetismo y Música. Aún más, cuando hablamos de estructuras más equipadas como las variedades diferenciables y los grupos de Lie, obtenemos algo similar a un Torsor, pero este recibe el nombre de espacio homogéneo, se dan ejemplos de ellos en Relatividad. 

Ricardo Cano
(UASLP)

Introduction to polysymplectic structures in Classical Field theories

In this talk, we will introduce in a constructive manner the basics of the so-called polysymplectic formalism for classical field theories with the aim to present the Poisson-Gerstenhaber bracket as fundamental to obtain the correct field equations by means of the De Donder-Weyl Hamiltonian.  Also, we will see the central role that $(n-1)$-forms play within this context as they characterize observables in a natural manner.  We will specify our ideas by considering the concrete example of the Yang-Mills field.

Alexis Tepale Luna
(BUAP)

Polysymplectic formulation of 3D Gravity with a Barbero-Immirzi like paramater

The goal of this talk is to show the Polysymplectic Hamiltonian approach applied to Bonzom-Livine action which is a model describing 3D Gravity with a Barbero-Immirzi like parameter.   Following Dirac's terminology, we shall present the complete set of constraints and applying Poisson-Gerstenhaber bracket among the $(n-1)$-forms constraints we show there are no first-class constraints within this new framework. Finally, we will recover Einstein 3D Equations by means of De Donder-Weyl Hamiltonian field equations.

Dulce María Valencia
(Northwestern U)

Electrostatic shape control of a charged molecular membrane from ribbon to scroll


Bilayers of amphiphiles can organize into spherical vesicles, nanotubes, planar, undulating, and helical nanoribbons, and scroll-like cochleates. These bilayer-related architectures interconvert under suitable conditions. Here, a charged, chiral amphiphile (palmitoyl-lysine, C16-K1) is used to elucidate the pathway for planar nanoribbon to cochleate transition induced by salt (NaCl) concentration. 

Victor Addi Amador Ortega
(BUAP)

Simetrías, sus estructuras algebraicas y la base de Cartan-Weyl

En la actualidad, hablar de física fundamental precisa imprescindiblemente del concepto de simetría. A pesar de tener un origen puramente matemático, geométrico y algebraico, hay simetrías presentes en manifestaciones naturales del universo e incluso de la conciencia humana, y la teoría de grupos surge como la herramienta matemática predilecta para estudiarla; con ella, la teoría de Lie de álgebras y grupos toma su lugar como uno de los pilares de la física moderna. La base de Cartan-Weyl es uno de los resultados importantes, e ingredientes indispensables para entender la física fundamental. En esta charla, se trata de clarificar el significado del concepto de simetría, su relación con las estructuras algebraicas y la íntima relación entre una Base de Cartan-Weyl con la física fundamental, dirigida a estudiantes de licenciatura.

Registration

Registration to the WMGP-UASLP20 is now CLOSED!  Thanks for your interest!

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Address

FACULTAD DE CIENCIAS, UASLP CAMPUS PEDREGAL
AV. PARQUE CHAPULTEPEC 1570, PRIVADA DEL PEDREGAL, SAN LUIS POTOSÍ, SLP,  MÉXICO.

Local Organizing Committee

Jasel Berra-Montiel
Alberto Molgado