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The talk is divided in 2 parts, the 1st part is for more general audience and the 2nd part is on current research.

Part 1: What is GIT? Why pencils of plane curves?
Abstract: I plan to first give a quick introduction to geometric invariant theory (GIT) as well as to describe what my motivation is for studying the problem that I will discuss in Part 2.

Part 2: On the GIT stability of pencils of plane curves
Abstract: In the second part of the talk, I will present a possible approach to the problem of classifying pencils of plane curves up to projective equivalence via geometric invariant theory. In particular, I will explain how the stability of a pencil is related to the stability of its generators, to the log canonical threshold, and to the multiplicities of a base point. And I will also discuss some relevant examples.