[Settfa] Fwd: a course of topos theory

[Wieslaw Kubis]

Dear all,

I'm forwarding the announcement of a short course that might be of 
interest to some of you.

Best wishes,

Wieslaw





Starting next Monday, Feb. 12, Amir Tabatabai will give a course 
consisting of seven to eight lectures on Topos theory. The lectures will 
take place in the Institute of Mathematics, lecture room in the rear 
building, from 14:00 to 15:30. They will also be streamed on zoom

zoom number: 472 648 284
passcode: 017 107

Title: "Topos Theory: a unified approach to independence"

Abstract: A topos is a category with some basic structure admitting a 
wide range of interesting interpretations. It can be a set-theoretical 
universe where the alternative types of mathematics take place, a 
generalized notion of space that lifts geometrical intuition far beyond 
the usual topological spaces or a syntax-free presentation of a 
first-order theory of some sort.  In this course on topos theory, we 
mainly focus on its first interpretation and its role in model 
construction, unifying techniques from forcing and Heyting-valued models 
to different types of realizability. We start with a very short and 
gentle introduction to category theory. Then, we introduce elementary 
toposes and as their concrete examples, we present the categories of 
sheaves and Heyting-valued sets, on the one hand, and the effective 
topos, on the other. Then, we move to the connection between topoi and 
logic to present a topos-theoretical version of some independence 
results including the independence of the continuum hypothesis and the 
axiom of choice. We also use toposes to realize some exotic, yet 
coherent possibilities including the so-called computable (resp. 
Brouwerian) universe in which all the functions on natural numbers 
(resp. real line) are computable (resp. continuous). These models are 
used to prove the consistency of Church-Turing thesis (resp. Brouwer's 
theorem on continuity of all functions on the reals) from intuitionistic 
arithmetic (resp. analysis).  Despite what it may appear at the first 
glance, the course only assumes familiarity with some basic concepts in 
first-order logic, algebra and topology and hence it must be accessible 
to all mathematics and computer science students. The rest, including 
the preliminaries on category theory, will be built during the course, 
whenever it’s needed.  We do not fix the number of lectures beforehand 
as it may change according to the audience and the topics they find more 
interesting. However, our rough estimate for the core material is eight 
lectures.

For more information including the references, the recorded video lectures
and any future change to the usual time and place of the course check
https://rb.gy/oexsbv [rb.gy]


Pavel Pudlak