Abstract: Let $H \subset \mathbb{C}^n$ be a complex hypersurface defined by a polynomial in $n$ variables over $\mathbb{C}$. $H$ may contain singularities, and it is classical to understand those singularities at a given point. In this talk, we introduce an algebraic invariant called the log canonical threshold, an invariant showing up in many different fields. We will see how computing the log canonical threshold relates to the resolution of singularities, and how we defined this notion in algebraic geometry via this relation. No algebraic geometry background is needed for this talk!
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