Title: Log canonical threshold and Newton distance

Abstract: The log canonical threshold (LCT) of a holomorphic function is an important invariant, providing a refined measure of the multiplicity of defined through the leading terms of its Taylor series expansion. Initially studied by Varchenko under the name complex singularity exponent, the LCT emerged naturally from his investigations into asymptotic expansions of integrals and mixed Hodge structures associated with vanishing cohomology. In this talk, we will introduce the analytic definition of the log canonical threshold and explore methods to compute it through illustrative examples.