Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
Developed by Denef-Loeser more than one decade ago, motivic Milnor fiber was a power tool to study singularities from the point of view of motivic integration. Especially, the impressive appearance of Kontsevich-Soibelman's theory of motivic Donaldson-Thomas invariants around 2008 two of whose foundations are the conjectural integral identity and the motivic Thom-Sebastiani theorem once again proves the importance of motivic Milnor fiber in different fields of mathematics. Recently, after works of Hrushovski-Loeser, one can describe motivic Milnor fiber in a more model-theoretical way. I used this new description to prove the integral identity conjecture for algebraically closed fields. More recently, during my visit at the ICTP in October 2013, using the same method, I was able to recover the motivic Thom-Sebastiani theorem. We shall introduce how to prove these results in the talk. Some comments on open problems concerning motivic Milnor fiber will be also given.
A. Bergamo
Speaker(s)
Le Quy Thuong (Vietnam National University, Hanoi)