Abstract: A frame (locale, complete heyting algebra) consist of a complete lattice
(A,≤, V, ∧,0,1)
in which the following distributive law holds:
α∧(VX) = V{α ∧ x | x ∈ X },
for everyX ⊆ A and α ∈ A. Frames are, in specific ways, algebraic manifestations of topological spaces. The ubiquitous example of a frame is the frame of opens of any topological space.
In this talk, we will see that in many algebraic phenomena there is a frame that controls certain process, (for instance the localizations of any Grothendieck category constitutes a frame), more over the point-free aspects of these frames served as a classification devices for many algebraic and topological situations.
Semblance: He obtained his doctorate at UNAM under the tutelage of Professor Jose Ríos Montes. Former FulBright Scholar Garcia Robles 2017-2018. Since 2019, he has been a full-time professor in the Mathematics Department of the University of Guadalajara. His research areas range between Abelian categories, module categories, tensor triangulated categories, and poin-free topology and its interaction between them.