This special ICTP Math Colloquium will be given by Prof. Carolina Araujo. The talk on Algebraic Geometry: history, applications and current trends will take place in the Euler Lecture Hall, on Thursday 13 June at 16.30 hrs and will be followed by light refreshments. Carolina Araujo was born in Brazil. She obtained her Ph.D in mathematics from Princeton University in 2004 and is currently a full Researcher at IMPA (Institute for Pure and Applied Mathematics), Rio de Janeiro, Brazil since 2017. Carolina's research field is Algebraic Geometry. She was an Affiliate member of the Brazilian Academy of Sciences from 2010-2014, an ICTP Simons Associate since 2015 and serves as Vice-president of the Committee for Women in Mathematics of the International Mathematical Union (IMU). Abstract: Algebraic Geometry is one of the oldest and most active fields of mathematics. It studies geometric objects that are defined by polynomials. These objects appear naturally in different sciences, and the study of their properties brings important applications to other areas of mathematics and beyond. In this talk, the speaker will give a general introduction to Algebraic Geometry, highlight some of its applications to other sciences, recent developments and guiding problems in the field. The event will be livestreamed from the ICTP website. Light refreshments will be served. All are welcome to attend.