Báo cáo viên: TS. Đinh Quý Dương
Thời gian: 16h30 Thứ Năm ngày 5/12/2024
Địa chỉ: Phòng 612 nhà A6 - Viện Toán học
Online: Join Zoom Meeting
https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1
Meeting ID: 996 3668 1387
Passcode: 123456
Abstract: Let X be a compact Riemann surface. A bundle E on X is called very stable bundle if it has no nonzero nilpotent Higgs field, and wobbly if it is stable but not very stable. Drinfeld - Laumon (1980s) and Donagi - Pantev (2009) have pointed out the significance of the wobbly locus in the context of the geometric Langlands correspondence. I will give a survey of recent results concerning wobbly bundles, roughly corresponding to three approaches to the study of this locus. In the first approach, one investigates the space of Higgs fields of a bundle E as a subspace of the moduli space of Higgs bundles; this approach, originally by Pauly - Peón-Nieto, was generalised by Hausel - Hitchin to the context of wobbly Higgs bundles. In the second approach, one investigates directly kernels of nilpotent Higgs fields which are subbundles of E; this is the approach taken by Pal - Pauly to prove Drinfeld's conjecture on the wobbly locus in the rank-2 case. In the third approach, one considers branched coverings S --> X and takes direct images of distinguished line bundles on S to produce wobbly bundles on X; this gives a rather simple criterion to produce wobbly bundles in the rank-2 case (arxiv:2406.04224). | 
