Time: 15h15, Friday, July 16, 2021

Join Zoom Meeting:

https://us02web.zoom.us/j/82772292046?pwd=Yyt5ZkpXa1AyNnlnbnk5VTdxVGkvZz09

Meeting ID: 827 7229 2046

Passcode: 830392

Abstract: In this talk, I review recent studies on the theory of algebraically closed value fields of equal charactersistic zero (ACVF theory) developed by Hrushovski-Kazhdan and Hrushovski-Loeser. More precisely, I consider a concrete Grothendieck ring of definable subsets in the VF-sort and prove the structure theorem of this ring which can be presented via materials from extended residue field sort and value group sort. One can construct a ring homomorphism HL from this ring to the Grothendieck ring of algebraic varieties, from which the motivic Milnor fiber can be described in terms of a certain definable subset in VF-sort. As applications, I sketch proofs of the integral identity conjecture and the motivic Thom-Sebastiani theorem using HL, as well as mention the recent work of Fichou-Yin in the same topic.

The seminar information can be found on the websites:

https://sites.google.com/ncts.ntu.edu.tw/agea-seminar

and/or

http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html