Singularities of Equidistants and Super Caustics in 3-Space (Graham Reeve)

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Singularities of Equidistants and Super Caustics in 3-Space

Plática dada por Graham Reeve (Liverpool Hope University, United Kingdom) en el evento Singularities in generic geometry and its applications: Valencia V, para celebrar el 60 aniversario de Federico Sánchez Bringas el jueves 3 de agosto del 2017 en el Auditorio Carlos Graef del Amoxcalli en la Facultad de Ciencias de la UNAM

Abstract:
I shall discuss the local geometry of a generic 1-parameter family of smooth surfaces in 3-space for which one member of the family has parallel tangent planes at two parabolic points with the additional property that their unique asymptotic directions are also parallel. I shall consider the equidistants of this family, that is the loci of points at a fixed ratio along chords joining points with parallel tangents, as a 2-parameter family depending on the value of the fixed ratio and on the parameter in the family of curves. This scenario gives rise to a so-called super caustic and is analogous to our previous works concerning planar super caustics. In the plane case the ”gull” singularity arose and in the present 3-dimensional work there appears a 3-dimensional equivalent gull singularity as well as some new classes. This is joint work with Peter Giblin.

Video de la plática
https://youtu.be/SwMuO8aWm-A

Foto de miniatura del video
https://photos.app.goo.gl/bF01DUZm0n7DPEMr2

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 Graham Reeve
grahamreeve86@gmail.com
https://www.hope.ac.uk/staff/reeveg.html
https://www.liverpool.ac.uk/mathematical-sciences/staff/graham-reeve/
https://www.researchgate.net/profile/Graham_Reeve2/info

Artículos publicados de Graham Reeve
https://link.springer.com/article/10.1134/S0081543812040165

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

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