One of the central challenges in singularity theory is to determine the analytic information encoded in a specific analytic invariant. In this presentation, we focus on the Bernstein-Sato polynomial, a discrete analytic invariant whose roots change discontinuously and abruptly depending on certain parameters. For plane branches, Blanco has recently identified a set of topological roots, that is, those that remain constant under singularity deformations within the same topological class. Today, it is still an open problem to understand what analytic information the remaining roots, the non-topological ones, carry. The main objective of this work has been to analyze what analytic information can be obtained from the Bernstein-Sato polynomial. Specifically, in the work presented, it has been shown that for genus 1 branches (that is, with a characteristic exponent), the non-topological roots determine the first non-topological value of the K\u00e4hler differentials, which corresponds to a translation of the Zariski exponent. Additionally, an example is given that allows demonstrating that no other non-topological value of the K\u00e4hler differentials can be recovered from the Bernstein-Sato polynomial<\/p>","protected":false},"featured_media":0,"parent":0,"template":"","categoria_sessions_conferences":[277],"class_list":["post-20972","conference","type-conference","status-publish","hentry","categoria_sessions_conferences-4a-jornada-tfm-2026"],"acf":[],"_links":{"self":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/conference\/20972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/conference"}],"about":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/types\/conference"}],"wp:attachment":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/media?parent=20972"}],"wp:term":[{"taxonomy":"categoria_sessions_conferences","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/categoria_sessions_conferences?post=20972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}