AbstractThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, this enables one to relate geometric structures on surfaces with algebraic geometry, and on the other hand, one obtains interesting hyper-Kähler metrics on the solution spaces. In my talk, I will explain how t...
AbstractThe real form problem asks how many different ways one can describe a given complex variety by polynomial equations with real coefficients, up to isomorphisms over the real number field. In this talk, I will discuss some recent results about smooth complex projective varieties with infinitely many real forms. This talk is based on joint works with T.-C. Dinh, C. Gachet, H.-Y. Lin, K. Og...
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