Hello everyone !
I’m Marine Cases, a first year undergraduate at Paris-Saclay University. I intend to learn as much mathematics as possible, since I love the idea of connecting different fields together. When I was reading Récoltes et Semailles, I was intrigued by what Alexandre Grothendieck considered his most unifying contribution : toposes. And some web searching later, that’s how I found out about Prof. Caramello’s bridges !
And I am now starting a small project on Stone duality under Prof. Olivia Caramello’s supervision !
So my midterm goal is to read « A topos-theoric approach to Stone-type dualities » and I am starting to read: « Frames and locales » ( Jorge Picardo and Aleš Pultr ), « Stone Spaces » (P. Jonhstone) and « Sheaves in Geometry and Logic » (Saunders MacLane and Ieke Moerdijk). I already know some category theory, commutative algebra, and I am following René Cori and Daniel Lascar books for logic.
Happy to be here !
Hello ! Welcome here ! I was too a student at Paris-Saclay, even though I'm leaving to do a PhD next year. I did also read the books by René Cori and Daniel Lascar during my undergraduate studies and I liked them very much, they were the books which made me interested in logic.
@elio-pivet Nice seeing a fellow saclay student here ! Yes they are really great books, and they have corrected exercises, which is better for self study.
So what is your PhD subject ?
My PhD will be about toposes representations by quantales (which are another generalization of locales) and quantaloids (which are quantales with several objects).
@estebanricardo22 Hi Esteban,
I make progress in very very slow pace at this moment since I’m extremely busy. I did reach sites on chapter 3 and I read Borceux ‘s very nice « Some glances at topos theory», that he wrote after Prof.Caramello’s invitation, after having read the also very nice and more basic « Introduction to topos theory » by Kostecki.
Given that Prof.Caramello’s theory is designed to cover a very very large array of mathematics, I’m also trying to extend my knowledge in other areas too so I have a mountain of books that I want to read, and "Sheaves in Geometry and Logic" is at the top but the mountain keeps on growing …