Department of Mathematics Calendar

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Graduate Student Homotopy Theory Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Altgeld Hall 345
Date
Oct 7, 2022   3:00 pm  
Speaker
Anthony D'Arienzo
Contact
Zachary Halladay
E-Mail
zah2@illinois.edu
Views
57

Title: Homotopical Ideas in First-Order Logic
Abstract: The interaction between logic and homotopy theory is dominated by higher category theory and type theories. However, recent developments in traditional first-order logic are being interpreted in an increasingly homotopical paradigm, leading to new Stone-duality-esque theorems by Makkai, Butz, Moerdijk, Lurie, and others. These results show that---while type theories have an internal homotopy theory---there exists an external homotopy theory of first-order theories. This talk is a survey of the history of categorical logic and its applications for homotopy theory, as well as a discussion on why these homotopical results are showing up in the first place.

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