Summer Topology Conference 2016

I have already said I would be at the Galway Colloquium in Leicester, UK, on Monday, August 1st, 2016. Right after that, I will participate to the 2016 Summer Topology Conference—same place, from Tuesday to Friday.

I will give a talk on Noetherian spaces. They form Section 9.7 of the book, and I will try to make an accessible introduction to the view expounded there, that they form a natural topological generalization of the notion of well-quasi-ordering. The pièce de résistance will be the topological Higman lemma, of which I will attempt to give a complete proof during the talk.  I will also talk about applications in computer science, finite representations of open and closed subsets, and the curious case of the powerset of a Noetherian space.  You can find the slides here.  See you there!

Galway Colloquium 2016

I will be at the Galway Colloquium at Leicester, UK, on Monday, August 1st, 2016.  I will give an introduction to T0 topology and domain theory there, aimed mostly at students in mathematics.

I will try to illustrate some of the key concepts in the field by progressing through a proof of Dana S. Scott’s theorem (1972) that the injective T0 spaces are the continuous lattices. This will be an opportunity to touch various subjects: dcpos, the specialization ordering, Sierpiński space, retracts, Stone duality, sober spaces and sobrification, b-spaces and algebraic posets, c-spaces and continuous posets, notably.

Have a look at the slides! Note that there are several grayed areas, which hide some of the proofs.  This is on purpose: I am expecting the attendees to find the missing arguments by themselves.  If you plan to come to Leicester, you may try to think about them in advance.  Otherwise, have fun and try to find the arguments by yourselves!  Note that most of the material is scattered through the book, too…