IV Escuela Doctoral Singularidades y Ecuaciones Diferenciales
IV Escuela Doctoral Singularidades y Ecuaciones Diferenciales
IV Escuela Doctoral Singularidades y Ecuaciones Diferenciales
Monday, 18 de January del 2016


Actividades y Eventos

5/10
De la PUCP al Perú: Huancavelica
H. Azabache, M. Martinez (PUCP)
Elaboración de objetos de aprendizaje usando Geogebra

Del 5 al 7 de octubre
Inscríbaseaquí

13/10
De la PUCP al Perú: Huaraz
A. Poirier
(PUCP)
Iteración de polinomios

Del 13 al 15 de octubre
Inscríbase aquí.

13/10
De la PUCP al Perú: Puno
C. Figueroa (PUCP)
Aplicaciones Armónicas

Del 13 al 15 de octubre
Inscríbase aquí.


Video Destacado
Charla del profesor José Manuel Aroca - Sección Matemáticas
Videoconferencia entre Valladolid y la UNSAAC (Cusco) a cargo del Dr. J.M Aroca, Director de las Escuelas Doctorales PUCP-UVa.
Video

Escuela CIMPA

Cursos

Course 1
Lecturer: José Manuel Aroca (Universidad de Valladolid, Spain, aroca@agt.uva.es )
Title: Grupoids, stacks, etc.
Abstract: As a complement of the Guy Casale course, I will present, in an elementary way, the Grothendieck viewpoint of the Galois theory.

Course 2
Lecturer: Percy Fernández (Pontificia Universidad Católica del Perú, pefernan@pucp.edu.pe )
Title: Transformation Groups of Holomorphic Foliations
Abstract: We study the automorphism group of a foliation on a projective. Along the course we study the structure of arbitrary codimension foliations on projective varieties invariant by an infinite linear algebraic group. We also study holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves.

Course 3
Lecturers: Lorena López (Universidade de Minas Gerais, Brazil, lorena@mat.ufmg.br ) and Javier Ribón (Universidade Federal Fluminense, Brazil, javier@mat.uff.br )
Title: Algebraic properties of groups of complex analytic local diffeomorphisms.
Abstract: A solvable group of complex analytic local diffeomorphisms in dimension one is metabelian. It is interesting to ask whether or not the derived length of a solvable group of local diffeomorphisms is bounded by a constant that depends only on the dimension. The answer is positive and it is possible to provide an assymptotically optimal upper bound. We can give the best possible upper bound for dimensions 2 and 3. The idea of the proof is replacing the initial solvable group with its algebraic closure and then studying well chosen actions of this group in finite dimensional vector spaces.

Course 4
Lecturer: Guy Casale (Univesité de Rennes I, France,  guy.casale@univ-rennes1.fr )
Title: Pseudo-groupes algebriques de transformations et theories de Galois
Abstract: Ce cours est une introduction au pseudo-groupe de Galois d'une application f de M dans M, rationnelle dominante sur une variété algébrique.
Le plan du cours est le suivant (il pourra être raccourci, le point 3 peut disparaître, suivant les connaissances mathématiques des participants)

  1. Définitions
    • Pseudogroupes
    • Espaces de jets
    • Pseudo-groupes algébriques et pseudogroupe de Galois
    • Premier exemples, pesudogroupes préservant une structure géométrique
    • Théorème de Chevalley pour les pseudogroupes algébriques.
  2. Le cas ou M est de dimension 1
    • Nous donnerons la liste des applications f ayant un petit pseudogroupe de Galois.
  3. Quelques remarques lorsque M est de dimension deux
  4. Les équations aux différences.
Les équations aux différences sont des exemples d'rationnelle dominante. Nous montrerons que  les équations résolubles par quadratures discretes ont un pseudogroupe de Galois résoluble.

Course 5
Lecturer: Julie Déserti (Université Paris VII, France, deserti@math.jussieu.fr )
Title: On the birational maps of the complex projective plane.
Abstract: I will introduce the basic tools which are useful to study such maps by presenting some
known properties of the Cremona group. The mentioned properties are algebraic properties: generators, relations, finite subgroups, subgroups of finite type, automorphisms of the Cremona group, Tits alternative... but also dynamical properties: classification of birational maps, centralizers of Cremona maps, dynamics of an Heisenberg subgroup and of course construction of automorphisms with positive entropy.

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