Abstract:

Topos theory is a branch of mathematics, based on category theory, which has connections to both algebraic geometry and mathematical logic. Within mathematical logic it can be used to give alternative, more flexible foundations for all of mathematics, and in particular provides the foundation for subjects such as synthetic differential geometry. More recently, the work of Olivia Caramello has shown that toposes can be used to provide bridges between distinct mathematical areas. The aim of this class is to provide an introduction to topos theory for those who have some elementary understanding of category theory and mathematical logic, with a goal of proceeding far enough (either this term or in the spring) to understand Caramello's programme.

Upcoming Talk:

Title: Geometric logic in Grothendieck toposes

Speaker: Nathan Carruth 卢天赐

Time: 12月5日星期二，下午5:30-6:30

Venue: 双清综合楼C645

Abstract: We will introduce Grothendieck toposes and show how some portions of the first-order categorical logic we have been discussing can be interpreted inside them. One resource we are following is https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf. 

Past Talks：

Title: Categorical logic
Speaker: Nathan Carruth 卢天赐
Time: 11月28日周二，下午5:30-6:30
Venue: 双清综合楼C645 

Abstract: We will continue our study of categorical logic and try to get to some concrete examples. One resource we are following is https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf.

Title: Categorical logic
Speaker: Nathan Carruth 卢天赐
Time: 10月31日周二，下午5.30到6.30
Venue: 双清综合楼C653

Abstract:

We will begin our introduction to (many-sorted) first-order predicate logic and the interpretation of various fragments of this logic in categories with sufficient structure. A reference is https://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf.

Title: Background: universal algebra
Speaker: Nathan Carruth 卢天赐
Time: 10月10日周二，下午5.30到6.30
Venue: 双清综合楼B627

Abstract:

We will finish talking about universal algebra and go on to propositional calculus, based on Chapters 1 and 2 of An Algebraic Introduction to Mathematical Logic by Barnes and Mack (https://link.springer.com/book/10.1007/978-1-4757-4489-7). 

Title: Background: universal algebra
Speaker: Nathan Carruth 卢天赐
Time: 9月26日周二，下午5:30到6:30
Venue: 双清综合楼C645 

Abstract:

We will discuss universal algebra (and possibly a bit of propositional calculus), based on Chapter 1 of An Algebraic Introduction to Mathematical Logic by Barnes and Mack (https://link.springer.com/book/10.1007/978-1-4757-4489-7).