From d299d6e219fe1fd946ba864e2c086a94a0f74e84 Mon Sep 17 00:00:00 2001 From: German Correa Date: Mon, 18 Dec 2017 18:11:26 -0300 Subject: [PATCH] Se agregan los pdfs de algunas charlas y se corrige la mesa redonda. --- pdfs/agonzalez.pdf | Bin 0 -> 260025 bytes pdfs/amaldonado.pdf | Bin 0 -> 56014 bytes pdfs/apereyra.pdf | Bin 0 -> 87108 bytes pdfs/arovella.pdf | Bin 0 -> 237413 bytes pdfs/eellis.pdf | Bin 0 -> 384793 bytes pdfs/egardella.pdf | Bin 0 -> 236456 bytes pdfs/fdalmao.pdf | Bin 0 -> 295278 bytes pdfs/hcastagna.pdf | Bin 0 -> 131732 bytes pdfs/mcaputi.pdf | Bin 0 -> 210533 bytes pdfs/promero.pdf | Bin 0 -> 317189 bytes pdfs/vmesa.pdf | Bin 0 -> 118239 bytes pdfs/vrumbo.pdf | Bin 0 -> 343518 bytes prgr/charlas.html | 104 +++++++++++++++++++++++------------------- prgr/cursos.html | 39 ++++++++-------- prgr/diplomados.html | 34 ++++++++------ prgr/mesaredonda.html | 35 ++++++++++++-- prgr/plenarias.html | 34 +++++++------- 17 files changed, 147 insertions(+), 99 deletions(-) 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    "Transformaciones en la enseñanza de la Matemática para estudiantes ingresantes a la Facultad de Arquitectura, Diseño y Urbanismo"

    -

    Omarg Gil - FADU

    +

    Omarg Gil - FADU

    Presentaré una estrategia de transformación de la enseñanza aplicada entre 2013 y 2017 en el curso de Matemática de la carrera de Arquitectura en la Facultad de Arquitectura Diseño y Urbanismo de la Universidad de la República, articulada en torno a los siguientes ejes: organización del aula en equipos de trabajo y enseñanza activa; contextualización de la Matemática en la formación del estudiante; atención a los aspectos afectivos y de vínculo en clase; aplicación de un sistema de evaluación con instancias individuales, grupales, autoevaluación y evaluación por pares, que ofrece oportunidades de revisión del trabajo; diversificación de la oferta de actividades; sistematización de la gestión y organización de los cursos; retroalimentación de la toma de decisiones a partir del seguimiento de los cursos, el análisis de las características de la población estudiantil y la evaluación de las políticas implementadas. Se constató una importante mejora del rendimiento de los estudiantes, evidenciada en la reducción del tiempo empleado en aprobar el curso de Matemática. Por otra parte, en las entrevistas realizadas, los estudiantes expresan satisfacción con los dispositivos grupales y por la mejor vinculación de los temas del curso con otros contenidos de su formación. Se discutirán también avances de resultados de la implementación del nuevo plan de estudios 2015, en el que ya ningún curso de Matemática es obligatorio, pero los estudiantes deben completar seis créditos en esta disciplina, escogiendo al menos uno de tres cursos con objetivos generales comunes pero objetivos específicos y contenidos netamente diferenciados. - Se presentarán algunos análisis prospectivos acerca de posibles líneas de profundización de la experiencia, que incluyen el desarrollo de programas de tutoría entre pares, la implementación de nuevos sistemas de orientación, seguimiento y apoyo a los estudiantes, la intervención sobre las estrategias de recursado de los estudiantes y el desarrollo de líneas de investigación sobre núcleos específicos de problemas emergentes de este programa de acciones. -

    + Se presentarán algunos análisis prospectivos acerca de posibles líneas de profundización de la experiencia, que incluyen el desarrollo de programas de tutoría entre pares, la implementación de nuevos sistemas de orientación, seguimiento y apoyo a los estudiantes, la intervención sobre las estrategias de recursado de los estudiantes y el desarrollo de líneas de investigación sobre núcleos específicos de problemas emergentes de este programa de acciones. +


    Construccion de laminaciones minimales por superficies hiperbolicas

    -

    Joaquín Brum - IMERL

    +

    Joaquín Brum - IMERL

    Mostraré como construir algunos ejemplos nuevos de laminaciones minimales, prestando particular atención a la topología @@ -27,7 +27,7 @@ geometría hiperbólica y convergencia de Gromov-Hausdorff entre espacios métricos. Esta es una charla pensada para estudiantes, definiré todos los - objetos que utilice. + objetos que utilice.

    Es un trabajo en conjunto con Sebastien Alvarez, Matilde Martinez y @@ -38,16 +38,16 @@

    "Noncommutative absolute neighborhood retracts"

    -

    Hannes Thiel - Universität Münster

    +

    Hannes Thiel - Universität Münster

    A compact metric space X is said to be an absolute neighborhood retract (ANR) if every continuous map from a closed subset K of a compact space Y to X can be extended to a neighborhood of K. This is a weak form of injectivity in the category of compact, metric spaces. Every manifold is an ANR, but not every space is an ANR. - + To X we associate algebra C(X) of continuous complex-valued functions on X. This is a C*-algebra with the supremum norm and pointwise operations. The categories of compact, metric spaces, and the category of commutative, unital, separable C*-algebras are (contravariantly) equivalent. In this sense, we think of C*-algebras as "noncommutative topological spaces". Using this correspondence to translate the concept of an ANR to (noncommutative) C*-algebras, we obtain a weak form of projectivity in the category of C*-algebras, called semiprojectivity. Thus, we think of semiprojective C*-algebras as the noncommutative absolute neighborhood retracts. - + A long-standing question asked to determine, in terms of X, when C(X) is semiprojective among all C*-algebras. Clearly X must be an ANR, but is that sufficient? Surprisingly, a dimensional restriction appears. We show that the following are equivalent: (1) C(X) is a semiprojective C*-algebra. (2) X is an ANR and its covering dimension is at most one. - + This solves a conjecture of Bruce Blackadar. This is joint work with Adam Soerensen (University of Oslo)

    @@ -55,9 +55,11 @@

    -

    "Un Diálogo entre la Conectividad y la Confiabilidad de Redes"

    -

    Pablo Romero - IMERL

    -

    +

    "Un Diálogo entre la Conectividad y la Confiabilidad de Redes" - + +

    +

    Pablo Romero - IMERL

    +

    Uno de mis mayores caprichos de este año fue buscar conexiones entre aspectos puramente determinísticos, como lo es la teoría de conectividad de redes, y otros puramente probabilísticos, como la confiabilidad de redes. La teoría extremal de grafos provee comunión entre ambos mundos. Como parte del corto camino trazado, se reconceptualizan trabajos de Gustav Kirchhoff, Frank Harary y Klaus Wagner. @@ -67,13 +69,15 @@


    -

    "Hay que volver a la raíz"

    -

    Federico Dalmao - DMEL

    +

    "Hay que volver a la raíz" - + +

    +

    Federico Dalmao - DMEL

    - El estudio de las raíces de ecuaciones y de ceros de funciones es uno de los más antiguos y transversales en la matemática. Hace cinco siglos Cardano, Tartaglia, Ferrari entre otros dieron algoritmos (y fórmulas) para hallar las raíces de las ecuaciones de tercer y cuarto grado. Hace dos siglos, Ruffini, Abel y Galois probaron la imposibilidad de expresar mediante radicales las soluciones de ecuaciones generales de quinto o mayor grado. + El estudio de las raíces de ecuaciones y de ceros de funciones es uno de los más antiguos y transversales en la matemática. Hace cinco siglos Cardano, Tartaglia, Ferrari entre otros dieron algoritmos (y fórmulas) para hallar las raíces de las ecuaciones de tercer y cuarto grado. Hace dos siglos, Ruffini, Abel y Galois probaron la imposibilidad de expresar mediante radicales las soluciones de ecuaciones generales de quinto o mayor grado. - Ya en el siglo XX, una de las formas de abordar el problema se expresa de la forma ¿dónde se ubican las raíces de una ecuación típica?,  ¿cuántas raíces reales tiene una ecuación típica?, etc. - Estas preguntas son ambiguas, ¿qué quiere decir típico?. En la década de 1930 comenzó el estudio de los ceros de polinomios aleatorios por Bloch, Pólya, Kac, Littlewood, Offord, etc. De esta forma, a grandes rasgos, se entiende por típico el promedio. De más está decir que desde entonces la literatura en el tema no ha parado de crecer.  + Ya en el siglo XX, una de las formas de abordar el problema se expresa de la forma ¿dónde se ubican las raíces de una ecuación típica?,  ¿cuántas raíces reales tiene una ecuación típica?, etc. + Estas preguntas son ambiguas, ¿qué quiere decir típico?. En la década de 1930 comenzó el estudio de los ceros de polinomios aleatorios por Bloch, Pólya, Kac, Littlewood, Offord, etc. De esta forma, a grandes rasgos, se entiende por típico el promedio. De más está decir que desde entonces la literatura en el tema no ha parado de crecer.  La charla está orientado a todo público. En ella se hará un recorrido por diferentes problemas vinculados a los ceros de polinomios y ondas aleatorios (número y ubicación, longitud y geometría de las curvas de nivel, etc) mostrando algunos resultados clásicos y también algunos recientes.

    @@ -81,7 +85,7 @@

    "Dendritaciones de superficie"

    -

    Alfonso Artigue - DMEL

    +

    Alfonso Artigue - DMEL

    Las dendritaciones son una generalización de foliaciones singulares en superficies desde el punto de vista de la teoría de continuos. El ejemplo base es la foliación estable de un difeomorfismo seudo Anosov. El objetivo de la charla es explicar la definición de esta estructura, dar ejemplos, resultados generales y mostrar aplicaciones al estudio de homeomorfismos con alguna forma de expansividad.

    @@ -91,7 +95,7 @@

    "La distancia de Gromov-Hausdorff, programación semidefinida y deep learning"

    -

    Soledad Villar – New York University

    +

    Soledad Villar – New York University

    Resumen: La distancia de Gromov-Hausdorff, definida en el conjunto de espacios métricos compactos modulo isometrías, fue introducida por Gromov como herramienta para probar su célebre teorema sobre crecimiento de grupos. Desde el punto de vista computacional, calcular la distancia de Gromov-Hausdorff es un problema difícil, incluso en espacios métricos finitos. En esta charla se explicará una técnica llamada programación semidefinida, y cómo utilizarla para aproximar localmente la distancia de Gromov-Hausdorff en espacios métricos finitos. Tambien se discutirán las propiedades topológicas de la distancia aproximada. Si el tiempo es suficiente se discutirá la aplicación nuevas técnicas, conocidas como 'deep learning' que muestran buenos resultados en la práctica pero su marco teórico es un problema abierto. @@ -102,10 +106,10 @@

    "Hacia nuevos modelos para la lógica y la matemática"

    -

    Alexandre Miquel - IMERL

    +

    Alexandre Miquel - IMERL

    La teoría de modelos tiene un papel muy importante en lógica, en la medida en que permite demostrar la consistencia o la independencia de algunos axiomas de la matemática (axioma de elección, hipótesis del continuo) relativamente a sistemas bien establecidos. El objetivo de esta charla (con destino a matemáticos no especialistas en lógica) es presentar los conceptos y problemas fundamentales de la teoría de modelos, así como algunas de las herramientas más avanzadas que se desarrollan en Montevideo. - + En una primera parte, recordaremos el marco fundamental de los modelos de Tarski (basados en el álgebra de Boole con dos elementos), así como algunas paradojas que surgen naturalmente en tal marco, a pesar de su simplicidad. Luego, mostraremos cómo se puede extender la noción de modelo, cambiando la noción de valor de verdad subyacente, e ilustraremos el interés de tal cambio con algunos ejemplos. Al final, presentaremos la noción de álgebra implicativa desarrollada en Montevideo, así como las perspectivas para la teoría de modelos.

    @@ -114,35 +118,39 @@

    "Sobre la conjetura de Mc.Duff sobre la C1 minimalidad de los conjuntos de Cantor"

    -

    Aldo Portela - IMERL

    +

    Aldo Portela - IMERL

    - En la teoría de sistemas dinámicos los conjuntos minimales son de gran - importancia. En la charla veremos como son los posibles conjuntos - minimales para un homeomorfismo que actua en el círculo. También - estudiaremos las posibilidades cuando el sistema dinámico se obtiene por - la acción de un difeomorfismo de clase C^1. En este caso, la conjetura - de McDuff da condiciones sobre un conjunto que implican la no - minimalidad de dicho conjunto. + En la teoría de sistemas dinámicos los conjuntos minimales son de gran + importancia. En la charla veremos como son los posibles conjuntos + minimales para un homeomorfismo que actua en el círculo. También + estudiaremos las posibilidades cuando el sistema dinámico se obtiene por + la acción de un difeomorfismo de clase C^1. En este caso, la conjetura + de McDuff da condiciones sobre un conjunto que implican la no + minimalidad de dicho conjunto.


    -

    "Modelos matemáticos para composición musical"

    -

    Verónica Rumbo - CMAT

    +

    "Modelos matemáticos para composición musical" - + +

    +

    Verónica Rumbo - CMAT

    ¿Es posible componer de forma automática música con determinado "estilo"? En esta charla se presentarán algunas herramientas que procuran capturar los rasgos comunes de un conjunto de obras musicales y utilizar lo aprendido para generar aleatoriamente nuevas composiciones. Veremos (y escucharemos) algunos de los resultados. - La charla está orientada a un público en general, aunque se recomienda tener nociones de probabilidad y estadística (correspondientes a un primer curso de probabilidad). + La charla está orientada a un público en general, aunque se recomienda tener nociones de probabilidad y estadística (correspondientes a un primer curso de probabilidad).


    -

    "Acciones de grupos, promediabilidad, y equivalencia orbital"

    -

    Eusebio Gardella – Universität Münster

    +

    "Acciones de grupos, promediabilidad, y equivalencia orbital" - + +

    +

    Eusebio Gardella – Universität Münster

    La noción de promediabilidad para grupos topológicos fue introducida por von Neumann en el contexto de la paradoja de Banach-Tarski, y desde entonces ha tenido muchas aplicaciones, fundamentalmente en análisis armónico y álgebras de operadores. En teoría ergódica, promediabilidad está íntimamente relacionada con el lema de Rokhlin. En esta dirección, Ornstein-Weiss y Dye demostraron que cualquier dos acciones libres y ergódicas de un grupo promediable en un espacio de probabildiad estándar (como el intervalo), son orbitalmente equivalentes. Es decir, acciones de grupos promediables son muy flexibles. El caso de acciones de grupos no promediables es mucho más rígido: varios resultados parciales en la literatura culminaron en el siguiente teorema de Epstein e Ioana: todo grupo no promediable admite una cantidad no numerable de acciones libres y ergódicas en un espacio de probabilidad estándar que no son orbitalmente equivalentes. @@ -154,7 +162,7 @@

    "El número de oro, geometría, álgebra y aritmética"

    -

    Gerardo González Sprinberg - Centro de Matemática UdelaR - Université Grenoble Alpes

    +

    Gerardo González Sprinberg - Centro de Matemática UdelaR - Université Grenoble Alpes

    Breve historia del número de oro. De Euclides a Klein, desarrollo en fracciones continuas de números racionales e irracionales, una introducción. @@ -168,7 +176,7 @@

    Rigidez y geometricidad de acciones de grupos de superficies sobre el círculo.

    -

    Maxime Wolff – Paris VI

    +

    Maxime Wolff – Paris VI

    Consideramos representaciones desde un grupo de superficie cerrada a Homeo^+(S^1). @@ -184,7 +192,7 @@

    "Conjuntos minimales para sistemas de funciones iteradas en S1"

    -

    Jorge Iglesias - IMERL

    +

    Jorge Iglesias - IMERL

    La idea del curso es, mediante ejemplos, clasificar desde el punto de vista topológico los conjuntos minimales para un sistema de funciones iteradas en S1 Se daran las definiciones básicas ( muy poca teoría), se construirán muchos ejemplos y se discutirá @@ -197,8 +205,8 @@

    "PML, a new proof assistant"

    -

    Christophe Raffalli - Université Savoie

    -

    +

    Christophe Raffalli - Université Savoie

    +

    Proof assistants allow to write and verify mathematical proofs or software using a computer. Many are available around the world (Coq, Agda, PVS, NuPrl, ...) and PML is the one we are developing. Why do we need one more? I will present PML features, gradually and illustrated with examples explaining why it is different (and hopefully better) than the other proof assistants. @@ -206,11 +214,13 @@


    - +

    -

    K-teoría bivariante y conjeturas de isomorfismo

    -

    Eugenia Ellis - IMERL

    +

    K-teoría bivariante y conjeturas de isomorfismo - + +

    +

    Eugenia Ellis - IMERL

    La K-teoría algebraica es un invariante útil para ciertas interrogantes de la topología algebraica.  En la teoría de operadores existen otras interrogantes que son facilitadas por la K-teoría topológica.  @@ -224,24 +234,24 @@

    "Un paseo por la complejidad en análisis numérico"

    -

    Diego Armentano - CMAT

    +

    Diego Armentano - CMAT

    La complejidad de un algoritmo es el número de pasos requeridos para pasar de un input a un output. El conocimiento de este número nos permitiría comparar distintos métodos y poder determinar cuáles son más eficientes. Sin embargo el estudio de la complejidad es un tema muy compicado del cuál se sabe muy poco, aún en problemas básicos como encontrar raíces de polinomios o valores propios de matrices. En esta charla daremos un paseo por distintos problemas y métodos, discutiendo en cada caso qué se sabe (o no se sabe) sobre la complejidad. A su vez mostraremos cómo este problema motiva preguntas interesantes en las distintas áreas de la matemática.


    - +
    - \ No newline at end of file + diff --git a/prgr/cursos.html b/prgr/cursos.html index 6dc83f3..e849107 100644 --- a/prgr/cursos.html +++ b/prgr/cursos.html @@ -4,34 +4,37 @@

    (curso orientado a docentes)

    -

    Observando Poliedros con una mirada moderna"

    +

    Observando Poliedros con una mirada moderna - + +

    Angel Pereyra - CMAT

    - +

    - El estudio de los poliedros empezó en la antigüedad. Ciertamente en la época de Euclides - ya se conocían todos los poliedros convexos regulares -los sólidos platónicos-, - pero la noción de regularidad no se habían explorado en profundidad. - Con el paso del tiempo se fueron descubriendo otras familias de bellos poliedros con regularidades - menos exigentes que las de los sólidos platónicos. En este cursillo se pretende mostrar cómo ciertas + El estudio de los poliedros empezó en la antigüedad. Ciertamente en la época de Euclides + ya se conocían todos los poliedros convexos regulares -los sólidos platónicos-, + pero la noción de regularidad no se habían explorado en profundidad. + Con el paso del tiempo se fueron descubriendo otras familias de bellos poliedros con regularidades + menos exigentes que las de los sólidos platónicos. En este cursillo se pretende mostrar cómo ciertas nociones básicas de la matemática moderna (grupos de simetría, acciones, dualidad, etc.) iluminan a esas familias de poliedros.

    - +

    -

    "Sobre el trabajo de Maryam Mirzakhani"

    -

    Andrés Sambarino - CNRS

    +

    "Sobre el trabajo de Maryam Mirzakhani"

    +

    Andrés Sambarino - CNRS

    En julio 2014 M. Mirzakhani (Teherán 1977- Stanford 2017) se convierte en la primer mujer en ganar la medalla Fields. El objetivo del mini-curso es dar un panorama general (orientado a un público no especializado en el área) sobre algunos trabajos que la llevaron a ganar este premio. El contexto cae dentro de la Teoría de Teichmüller, punto de intersección entre el Análisis Complejo, los Sistemas Dinámicos y la Geometría Diferencial.

    - +

    -

    "Introducción a las álgebras de Lie"

    -

    Ana Gonzalez - IMERL

    +

    "Introducción a las álgebras de Lie" - +

    +

    Ana Gonzalez - IMERL

    En el año de 1873, Sophus Lie dio origen a las ideas que conforman la hoy denominada teoría de Lie, con aportes posteriores de Weyl, Cartan, Chevalley, Killing, @@ -59,20 +62,20 @@ ducción de la teoría básica del álgebra abstracta, hasta llegar a los resultados buscados en las álgebras de Lie. Fianlizaremos dando algunas aplicaciones en Física y economía y finanzas.

    - +

    -

    "Un paseo por la optimización"

    -

    Marcelo Fiori - IMERL

    +

    "Un paseo por la optimización"

    +

    Marcelo Fiori - IMERL

    Un problema de optimización es encontrar el mínimo de una función f sobre un conjunto X, así como el x* donde se alcanza. Vamos a comentar algunos aspectos teóricos y algunos métodos de optimización (es decir, sucesiones definidas en X que convergen a x*), y con esto como excusa, vamos a recorrer diferentes áreas y aplicaciones, desde estimadores de máxima verosimilitud a métricas riemannianas, pasando por grafos, flujos de gradiente, y valores propios.

    - +

    - + diff --git a/prgr/diplomados.html b/prgr/diplomados.html index f643f17..5ccd71d 100644 --- a/prgr/diplomados.html +++ b/prgr/diplomados.html @@ -5,47 +5,55 @@

    (orientado a docentes)

    -

    "¿Aprender a defraudar o a detectar fraude? Aplicaciones de la Ley de Benford"

    -

    María Caputi

    +

    "¿Aprender a defraudar o a detectar fraude? Aplicaciones de la Ley de Benford" - + +

    +

    María Caputi

    La Ley de Benford establece, contrariamente a la intuición, que, en algunos conjuntos de datos numéricos, la frecuencia de aparición del primer dígito significativo no es uniforme. La frecuencia con la que aparece cada dígito sigue una proporción particular que se explicita en la denominada por Benford en 1938 como “Ley de los números anómalos”. El 1 aparece como primer dígito significativo un 30,1% de las veces, el 2 un 17,6%, el 3 un 12,5%, el 4 un 9,7%, el 5 un 7,9%, el 6 un 6,7%, el 7 un 5,8%, el 8 un 5,1% y el 9 un 4,6%, aproximadamente. Esta ley permaneció como una mera “curiosidad estadística” por varias décadas. En 1992 fue catapultada a la luz e interés público por el contador norteamericano Mark Nigrini, quien en su tesis de doctorado la utilizó para detectar fraudes en las declaraciones fiscales. Se analizan varios métodos estadísticos para analizar si un conjunto de datos sigue o no la Ley de Benford. Se ejemplifican dichos métodos con conjuntos de datos clásicos que siguen la ley y se analiza cumplimiento de la Ley de Benford en los resultados del censo realizado en Uruguay en 2011. -

    +


    (orientado a docentes)

    -

    Criptografía sobre Curvas Elípticas

    -

    Horacio Castagna

    +

    Criptografía sobre Curvas Elípticas - + +

    +

    Horacio Castagna

    Los temas vinculados a la seguridad son de preocupación mundial. En particular, la seguridad en las comunicaciones y el ciberespacio. En el presente trabajo presentamos de manera sencilla las ideas básicas que están detrás de los métodos involucrados en la protección de las comunicaciones y los datos. En particular trataremos los aspectos teóricos referentes a las curvas elípticas, y cómo éstas pueden usarse para implementar algoritmos de codificado, cifrado y firma digital de documentos. Además construiremos un ejemplo sencillo, para ilustrar el mecanismo de protección de datos en una comunicación. -

    +


    (orientado a docentes)

    -

    "Un proyecto de intervención a partir de tareas de generalizar y particularizar: trabajo colaborativo entre investigador y formador de profesores"

    -

    Victoria Mesa

    +

    "Un proyecto de intervención a partir de tareas de generalizar y particularizar: trabajo colaborativo entre investigador y formador de profesores" - + +

    +

    Victoria Mesa

    Se presentará una intervención en Matemática Educativa llevada a cabo, en el marco del Diploma en Matemática (IPES–UdelaR), en conjunto con un docente de Profundización en Geometría en torno a la creación e implementación de actividades de particularizar y generalizar sobre el concepto de baricentro. El proceso vivenciado permitió constatar que las actividades de generalizar y particularizar un problema o enunciado matemático, pensadas como actividades de final abierto en una metodología de clase que fomente la producción del conocimiento matemático por parte del estudiante, favorecen que los estudiantes de profesorado de Matemática vinculen los conocimientos que aprenden en sus clases de Matemática de la carrera con los que deberán enseñar en enseñanza media. -

    +


    (orientado a docentes)

    -

    "Las tareas enfocadas en similitudes y diferencias en el aprendizaje de las transformaciones lineales en la formación inicial de profesores de Matemática"

    -

    Ana Maldonado

    +

    "Las tareas enfocadas en similitudes y diferencias en el aprendizaje de las transformaciones lineales en la formación inicial de profesores de Matemática" - + +

    +

    Ana Maldonado

    En el marco del Diploma en Matemática mención Enseñanza (ANEP-UdelaR) se realiza un proyecto de investigación en Matemática Educativa que intenta contribuir a la mejora de la enseñanza de las transformaciones lineales en la formación inicial de profesores de matemática. Para lograr tal propósito, se diseñaron actividades enfocadas en similitudes y diferencias considerando que estas permiten generar cierto grado de incertidumbre en el estudiante. Se realizó la experimentación de una de las actividades y se analizó la producción matemática de los estudiantes centrándose en la elaboración de conjeturas y el establecimiento de conexiones entre conceptos. -

    +

    - + diff --git a/prgr/mesaredonda.html b/prgr/mesaredonda.html index d543231..3e9ea5b 100644 --- a/prgr/mesaredonda.html +++ b/prgr/mesaredonda.html @@ -5,17 +5,42 @@

    -

    "Nuevos planes de estudio y contenidos de cursos de matemática en UdelaR"

    +

    "Nuevos planes de estudio y contenidos de cursos de matemática en UdelaR"

    Oradores:
    Roberto Markarian (Rector UdeLaR)
    Omar Gil (Facultad de Arquitectura)
    Gonzalo Tornaria (Facultad de Ciencias)
    -
    Paola Bermolen (Facultad de Ingenieria)
    -

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- +
Marcelo Fiori (Facultad de Ingenieria)
+ +

+
+
Moderador:
+
Fernando Pelaez (Prorector de educación UdelaR)
+

-

+ En la Facultad de Ciencias, Ingeniería y Arquitectura se han dado + recientemente importantes cambios en los programas, contenidos y + puesta en práctica de los cursos de Matemática. En la Facultad + Ciencias se ha rediseñado completamente la carrera, haciéndola más + flexible y diversificada. En Ingeniería, con notorios problemas de + masificación y egreso, se han rediseñado completamente los cursos de + cálculo. En Arquitectura, finalmente, ha habido transformaciones en + la didáctica y dinámica en el aula, innovadoras si las comparamos con + la práctica tradicional o histórica. Muchos de esos cambios + (entendemos) se imponen por varios motivos: (i) urgencia nacional en + mejorar el egreso y la calidad de la enseñanza terciaria. (ii) + influencia de transformaciones y tendencias mundiales. (iii) el aporte + del notorio crecimiento y profesionalización de la comunidad + Matemática uruguaya. La idea es discutir los cambios, los resultados + y su medición, y los desafíos a futuro. +

+

+ Cada orador tiene 15 minutos (justos) para exponer. Luego de las + exposiciones habrá una sesión de discusión que incluye las inquietudes + del moderador y preguntas del público (que se juntan durante las + exposiciones). +


diff --git a/prgr/plenarias.html b/prgr/plenarias.html index f1a5ce1..349c762 100644 --- a/prgr/plenarias.html +++ b/prgr/plenarias.html @@ -5,32 +5,34 @@

-

Dinamica de cubrimientos del anillo

-

Alvaro Rovella - CMAT

+

Dinamica de cubrimientos del anillo - + +

+

Alvaro Rovella - CMAT

Abundan resultados acerca de la dinámica unidimensional y de los homeomorfismos del anillo u otras superficies,  pero no así de los mapas no invertibles en dimensión dos. En esta charla se trata de mostrar algunos resultados  relativos a los cubrimientos del anillo abierto, generalizando algunos conceptos útiles como el número de rotación  y las semiconjugaciones con dinámicas supuestamente más conocidas. Se explicarán unos pocos teoremas pero  muchos ejemplos y preguntas.  -

+


-

Holomorphic curves and celestial mechanics

-

Umberto Hryniewicz - Universidade Federal do Rio de Janeiro

+

Holomorphic curves and celestial mechanics

+

Umberto Hryniewicz - Universidade Federal do Rio de Janeiro

We would like to describe how the modern methods of symplectic topology, such as pseudo-holomorphic curve theory, can be used to study celestial mechanics. Particular emphasis will be given to the planar circular restricted three-body problem. When the value of the Jacobi constant is high enough, components of the energy level covering a bounded Hill region are amenable to both Levi-Civitta or Moser regularization. Both schemes yield contact-type energy levels, allowing for the use pseudo-holomorphic curves. We will address a conjecture of Birkhoff asserting that the lift of a retrograde orbit via Levi-Civita bounds a disk-like global surface of section, and describe a version of the Poincare-Birkhoff theorem for Reeb flows which applies in the presence of a Hopf link of periodic orbits. If time permits we shall describe general results on the existence of genus zero global surfaces of section. -

+


-

Experiencias en matemática aplicada a la ingeniería de redes

-

Fernando Paganini - ORT

+

Experiencias en matemática aplicada a la ingeniería de redes

+

Fernando Paganini - ORT

Las aplicaciones de la matemática obligan a traspasar los límites de sus subdisciplinas. Así, en problemas de ingenería de redes (telecomunicaciones, @@ -43,30 +45,30 @@ teoría de colas con la teoría de control, aplicados al tráfico en Internet, los servicios de computación en la nube, y la regulación inteligente de cargas de potencia. -

+


-

Solución de las ecuaciones de Hamilton-Jacobi como límite clásico de integrales con respecto al Movimiento Browniano

-

Rafael León Ramos - IMERL

+

Solución de las ecuaciones de Hamilton-Jacobi como límite clásico de integrales con respecto al Movimiento Browniano

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Rafael León Ramos - IMERL

Se presenta un enfoque simplificado del problema de obtener la mecánica clásica a partir de una ecuación de difusión. Al final presentaremos una lista de ejemplos que incluye: el comportamiento de una partícula en un campo electromagnético y también una aproximación informal al comportamiento de la solución de la ecuación de onda, en el límite de altas frecuencias. -

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Charlando sobre geometría biracional

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Iván Pan - CMAT

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Charlando sobre geometría biracional

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Iván Pan - CMAT

De manera informal, estudiar geometría en un conjunto X significa fijar un grupo G de biyecciones e investigar qué propiedades permanecen invariantes bajo la acción de elementos de G. Si X admite estructura adicional (espacio topológico, variedad diferenciable, variedad algebraica, etc), se puede elegir G=G_X como siendo constituido por los isomorfismos en relación a dicha estructura (resp. homeomorfismos, difeomorfismos, automorfismos, etc). Si X es una variedad algebraica, en la topología subyacente de X todo abierto no vacío es esencialmente denso, por lo tanto dos automorfismos que coincidan en un abierto son iguales, i.e., la estructura geométrica de X es muy rígida. Por lo tanto, si se quieren entender propiedades de X que sean de naturaleza local (y entonces globales salvo en un conjunto "pequeño") en natural permitir que G_X contenga aplicaciones del tipo Φ:U V, con Φ isomorfismo y U, V dos abiertos densos de X; en términos algebraicos, y expresándose de modo impreciso, eso corresponde a estudiar propiedades de un dominio de integridad que sólo dependen de su cuerpo de fracciones. En este caso estamos estudiando la llamada Geometría Birracional de X. En esta charla, en la cual no pretendemos entrar en tecnicismos y en general argumentaremos utilizando conceptos básicos de álgebra y geometría, y apelando a la intuición, comenzaremos dando nociones generales sobre Geometría Birracional y una muy somera descripción del problema de clasificación de los pares (X,G_X), objeto de intensa investigaci\'on actualmente. Luego nos concentraremos en el caso en que X es una variedad lineal, que como veremos, su simplicidad contrasta con el hecho de que su geometría birracional (i.e. G_X) sea la más complicada, y casi completamente desconocida si X tiene dimensión mayor que dos. También veremos aplicaciones al estudio de foliaciones holomorfas y derivaciones en anillos de polinomios. -

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