2018 Intercity Geometry Seminar

The spring 2018 Intercity Geometry Seminar will be held around Mirror Symmetry and moduli spaces of Higgs bundles. We will be following a recent preprint of Grochenig, Wyss and Ziegler in which they prove a conjecture of Hausel and Thaddeus on the Hodge numbers of these moduli spaces. Announcements will be sent out via the am-l mailing list. We will be posting an outline of the seminar below, which will be updated and adjusted as we progress. If you want to volunteer a presentation, please contact David Holmes, Arne Smeets or Chris Lazda.

March 9 - Nijmegen

Lectures all take place in Room HG00.068 of the Huygens Building.

13:00 - 14:00 Andrey Soldatenkov
Introduction to the Hausel-Thaddeus conjecture
Abstract: Special Lagrangians and the SYZ fibration, mirror partners via hyperkähler rotations, relationship between Hodge numbers.
References: [HT03].
14:30 - 15:30 Arne Smeets
\(p\)-adic integration and point counting
Abstract: \(p\)-adic manifolds, gauge forms and measures, integration, structure of residue discs and relationship with point-counts.
References: [Igu00] §2,7 [Wei82].
16:00 - 17:00 Johan Commelin
Birational Calabi-Yau varieties have the same Betti numbers
Abstract: The Weil conjectures and the link between point-counting and Betti numbers, Batyrev's proof that birational Calabi-Yau's have equal Betti numbers via \(p\)-adic integration.
References: [Bat99].

April 13 - Leiden

Lectures all take place in Room 407-409 of the Snellius Building.

May 4 - Amsterdam

Lectures all take place in Room A1.04 at Science Park 904.

May 25 - Utrecht

Lectures all take place in Room MIN 2.02 of the Minnaert Building.

References

[Bat99] Batyrev - Birational Calabi-Yau \(n\)-folds have equal Betti numbers.

[GWZ17] Grochenig, Wyss, Ziegler - Mirror symmetry for moduli spaces of Higgs bundles via \(p\)-adic integration.

[HT03] Hausel, Thaddeus - Mirror symmetry, Langlands duality, and the Hitchin system.

[Igu00] Igusa - An introduction to the Theory of Local Zeta Functions.

[Wei82] Weil - Adeles and Algebraic Groups.