Abstract. In this talk I am going to introduce the concept of pure gaps in two points in a function field and show how they can be obtained from a generating set of the Werierstrass semigroup in two points. A complete characterization of the Weierstrass semigroup in two points over a Kummer will be given. Later on we apply these results to construct codes over certain Kummer extensions with many rational points.

Biography. Luciane Quoos received the M.Sc. and Ph.D. degrees in mathematics from the Instituto Nacional de Matemática Pura e Aplicada (IMPA), Brazil, in 1995 and 2000, respectively. In 1998, she joined the Instituto de Matemática, Universidade Federal do Rio de Janeiro, where she is currently a Full Professor. During a nine-month period, starting in August 2002, she held an European Research Consortium for Informatics and Mathematics (ERCIM) Post-Doctoral Fellowship at the Norwegian University of Science and Technology. In 2016, she spent her sabbatical at the Università degli Studi di Perugia, Italy. Her research interests include maximal curves and curves with many rational points over finite fields, Weierstrass semigroups, and algebraic geometric codes.