AbstractIt is attractive to classify Fano varieties with various types of singularities that originated from the minimal model program. For a Fano variety, the Fano index is the largest integer m such that the anti-canonical divisor is Q-linearly equivalent to m times some Weil divisor. For Fano varieties of various singularities, I show the Fano indexes can grow double exponentially with respe...
AbstractThe goal of this minicourse is to introduce the recent advances in Hodge theory via o-minimal techniques. We will start by revisiting the basics on o-minimal geometry with a view towards algebraization theorems (Pila-Wilkie counting theorem; o-minimal Chow and GAGA theorems in definable complex analytic geometry). In the realm of Hodge theory, we will explore several applications: (i) t...
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