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Model Theory Seminar | Mathias Stout (McMaster University)
	
 Sep 19, 2025 
 12:30PM to 1:30PM





	





























Date/Time

Date(s) - 19/09/2025
12:30 pm - 1:30 pm





Speaker: Dr. Mathias Stout (McMaster University)


Location: Hamilton Hall, Room 410


Title: Integration in Hensel minimal fields


Abstract: Motivic integration was introduced by Kontsevich in the nineties to show that biratonially equivalent Calabi-Yau varieties have the same Hodge numbers. His fruitful idea was quickly picked up and further developed first by Denef-Loeser and then by many others. In particular, one has the model-theoretic frameworks of Cluckers-Loeser and Hrushovski-Kazhdan, respectively. A key common point of these theories is that they provide Ax-Kochen/Ersov-type statements for integrals. On the other hand, they differ in which fields they apply to and how the ‘integral’ is represented.


In this talk, I will explain how to build a Hrushovski-Kazhdan style integral in Hensel minimal fields, thereby generalizing the original V-minimal setting. Similarly to Hrushovski-Kazhdan, we also have a version of this integral “without measures”, which classifies definable sets up to definable bijections, relative to the residue field and value group.


Additionally, since the abstract tameness notion of Hensel minimality also encompasses the discretely valued fields considered by Cluckers and Loeser, this opens the door for a precise comparison between the two frameworks.