On the motives of moduli space of parabolic Higgs bundles
Người báo cáo: Đỗ Việt Cường (Đại học Khoa học Tự nhiên, Hà Nội)
Speaker: Đỗ Việt Cường (Đại học Khoa học Tự nhiên, Hà Nội)
Time: 16:30 pm, 20 November
Venue: Room 612, A6, Institute of Mathematics-VAST
Online (Join Zoom Meeting) tại link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1
Abstract: Parabolic Higgs bundles were introduced by Simpson as a natural object to consider extending non-abelian Hodge theory to punctured Riemann surfaces. In “Mirror symmetry, Langland duality, and the Hitchin system, Invent. Math. 153 (2003) (1), 197-229”, Hausel and Thaddeus conjectured that the $E$-polynomial of moduli space $mathal{M}_{n,d}^w$ of parabolic Higgs bundles of rank $n$, degree $d$ and generic weight $w$ is independent of both the degree and the generic weight.
In this talk, I will explain how we can use the technique of motivic integration which is introduced in the work of Clucker and Loeser (Constructible motivic functions and motivic integration, Invent. Math. 173 (2008), 23-121) to prove that the class of $mathal{M}_{n,d}^w$ Â in the Grothendieck ring of rational Chow does not depend on $d$ and $w$. As a result, we confirm the conjecture of Hausel and Thaddeus.
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