Abstract：The theory of complements was introduced by Shokurov when he investigated log flips on threefolds, which turns out to be a very powerful tool in birational geometry. For a Fano fibration from X to Z with X being $\epsilon$-log canonical, Shokurov proposed a conjecture on the boundedness of klt complements, i.e. the existence of klt n-complements for some bounded natural number n. When...
AbstractWe briefly review the origin in physics of attractor points on the moduli space of Calabi-Yau threefolds. We turn to their mathematical interpretation as special cases of Hodge loci. This leads to fascinating conjectures on the modularity of the Calabi-Yau threefolds at these points in terms of their periods and L-functions. For hypergeometric one-parameter families of Calabi-Yau threef...
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