Geometria em Lisboa Seminar   RSS

21/02/2017, 16:30 — 17:30 — Room P3.10, Mathematics Building
André Gama Oliveira, Centro de Matemática da Universidade do Porto

Parabolic Higgs Bundles and Topological Mirror Symmetry

In 2003, T. Hausel and M. Thaddeus proved that the Hitchin systems on the moduli spaces of $\operatorname{SL}(n,\mathbb{C})$- and $\operatorname{PGL}(n,\mathbb{C})$-Higgs bundles on a curve, verify the requirements to be considered SYZ-mirror partners, in the mirror symmetry setting proposed by Strominger-Yau-Zaslow (SYZ). These were the first non-trivial known examples of SYZ-mirror partners of dimension greater than $2$.

According to the expectations coming from physicists, the generalized Hodge numbers of these moduli spaces should thus agree — this is the so-called topological mirror symmetry. Hausel and Thaddeus proved that this is the case for $n=2,3$ and gave strong indications that the same holds for any $n$ prime (and degree coprime to $n$). In joint work in progress with P. Gothen, we perform a similar study but for parabolic Higgs bundles. We will roughly explain this setting, our study and some questions which naturally arise from it.

Current organizer: Rosa Sena Dias