Αγαπητοί Συνάδελφοι, Φοιτητές και Φίλοι,
Θα θέλαμε να σας ενημερώσουμε ότι τη Παρασκευή 9 Δεκεμβρίου στις 12:00 στην αίθουσα Μ2 και στο πλαίσιο του Σεμιναρίου Γεωμετριας, θα δώσει ομιλία ο Ραφαήλ Τσιάμης (Harvard University).
Περίληψη: Hyperkahler manifolds have several analytic and algebraic properties making them accessible for description but difficult to construct. A construction of P. Kronheimer [3] gives an example of hyperkahler structure abstractly constructed on the cotangent bundle $T^\ast G_\mathbb{C}$ of the complex Lie group $G_\mathbb{C}$ corresponding to a compact Lie group $G$. This hyperkahler structure emerges through infinite dimensional reduction (hyperk\”ahler reduction) of the space of solutions of the so-called “Nahm equations”, and so its description is particularly difficult even for basic Lie groups. We present a partial description of the family of Kahler structures on $G_\mathbb{C}$ as complex submanifold of $T^\ast G_\mathbb{C}$ in the general case, extending a result of Stenzel [5] for homogeneous spaces. We then focus on $G=SU(2)$, for which $G_\mathbb{C}=SL(2,\mathbb{C})$; our calculation, method and results partially generalize a calculation of Dancer [1]. This is work in collaboration with Richard B. Melrose (MIT) and Michael Singer (UCL).
[3] P.B. Kronheimer, The hyperkähler structure on the cotangent bundle of a complex Lie group. MSRI preprint (1998).
[5] M. Stenzel, Ricci-flat metrics on the complexification of a compact rank one symmetric space. Manuscripta Math. (80), 151-163 (1993).
Zoom link:https://authgr.zoom.us/j/94933117785?pwd=VS9hOHMxMXB1bkUvem5HMWpFaTlvUT09
Meeting ID:949 3311 7785
Passcode: 093582
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