G-structures and singularities of map-germs
Plática dada por Shyuichi Izumiya (Hokkaido University) en el evento Singularities in generic geometry and its applications: Valencia V, para celebrar el 60 aniversario de Federico Sánchez Bringas en agosto del 2017 en el Auditorio Carlos Graef del Amoxcalli en la Facultad de Ciencias de la UNAM
Abstract:
We consider equivalence relations among smooth section-germs of vector bundles with respect to structure groups. One of these equivalence relations is the G-equivalence among smooth map germs introduced by Tougeron [5]. Alltough Gervais [1, 2, 3] investigated some properties of G-equivalence, there are no proper examples in their contexts. We give several interesting applications including quantum chemistry and spintronics [4], which are expected to have an application to the theory of topological insulators and so on. We emphasize that we can open a door for new important applications of singularity theory. Moreover we define other equivalence relations with respect to structure groups of vector bundles. Since a vector space can be identified with the tangent space of itself, we can consider the structure group of the vector bundle as a G-structure of the fiber (the vector space).
Then we discover that there are a lot of previous applications or new applications of the theory of singularities as examples of these equivalence relations. Some of these equivalence relations are geometric subgroups of A or K in the sense of Damon. However, some of them are not.
References
[1] J. J. Gervais, Suffuciency of jets. Pacific Journal of Mathematics, 72, 419–422, (1977)
[2] J. J. Gervais, G-stability of mappings and stability of bifurcation diagrams. J. London Math. Soc. 25, 551–563, (1982)
[3] J. J. Gervais, Deformations G-verselles et G-stables. Can. J. Math. XXXVI, 9–21, (1984)
[5] J. C. Tougeron, Ideaux fonctions differentiables. Springer-Verlag, Berlin, Heiderberg, New York 1972
Video de la plática
https://youtu.be/tfIDtscULEI
Foto de miniatura del video
https://photos.app.goo.gl/rep1hkUBJBTDdXpx2
Página del evento Singularities in generic geometry and its applications: Valencia V, para celebrar el 60 aniversario de Federico Sánchez Bringas
http://geogen.fciencias.unam.mx
Programa del evento
http://geogen.fciencias.unam.mx/On-line/program28JULIOIV.pdf
Resúmenes de las pláticas
http://geogen.fciencias.unam.mx/Abstracts/TalksandAbstracts.pdf
Cartel evento
https://goo.gl/photos/28EfgbZn6FyzVXEk7
Foto del evento
https://goo.gl/photos/2ZzpcGxaPW7M97n79
Paginas de Shyuichi Izumiya
http://www.math.sci.hokudai.ac.jp/en/resercher/izumiya-en.php
https://researchers.general.hokudai.ac.jp/profile/en.NhI6vN41qjXe2I4jhBwKRA==.html
https://www.researchgate.net/profile/Shyuichi_Izumiya
http://publicationslist.org/izumiya
http://researchmap.jp/izumiya/?lang=english
Otras pláticas del evento Singularities in generic geometry and its applications: Valencia V, para celebrar el 60 aniversario de Federico Sánchez Bringas
https://www.youtube.com/playlist?list=PLiD-IJzweXR866QuMLRYm-FF-mCVogVRn
Página de facebook del Ciencias TV
https://www.facebook.com/Ciencias-TV-…
Videos de matemáticas en Ciencias TV
https://www.youtube.com/playlist?list…
Página de facebook del Ciencias TV
https://www.facebook.com/Ciencias-TV-…
Videos Académicos de matemáticas (pláticas grabadas)
https://www.youtube.com/playlist?list…
Videos Académicos publicados
https://www.youtube.com/playlist?list…
Videos Académicos publicados en 2017
https://www.youtube.com/playlist?list…
Album de fotos miniatura de los videos Académicos publicados en 2017
https://goo.gl/photos/7yKCos9N8T9SecGk9
Videos Académicos publicados en 2016
https://www.youtube.com/playlist?list…
Album de fotos miniatura de los videos Académicos publicados en 2016
https://goo.gl/photos/Wk45yoGqPe5hKTw77
Videos Académicos publicados en 2015
https://www.youtube.com/playlist?list…
Videos Académicos publicados en 2014
https://www.youtube.com/playlist?list…
Videos Académicos publicados en 2013
https://www.youtube.com/playlist?list…
Agradecemos apoyo de
Erick Tovar quien grabo la platica
Facultad de Ciencias de la UNAM
http://www.fciencias.unam.mx/