 Between the period 1997-2002 Conca was a Titular Member of the Commission of Academic Evaluation of the Faculty of Physical and Mathematical Sciences of the University of Chile; and was President from 2001-2003.Conca has been invited to give classes and lectures at many prestigious schools internationally including Spain, Ecuador, France, Brazil and in other cities throughout his native Chile.He has been invited to dictate Plenary and Inaugural Conferences at various International Congresses of Mathematics such as at the "Italian-Latinoamerican Conference on Applied and Mathematics" in Rome in 1998, at the 26th "French National Congress on Numerical Analysis", at Ardèche later that year, the 4th World Congress on Computational Mechanics, Buenos Aires (1998), the 1st International Congress on Asymptotic Analysis of Average Heterogeneous Structures, St. Petersburg (2001), the 1st Latin America Congress of Mathematicians, in Rio de Janeiro (2000), the XVII ' National Spanish Congress on Differential Equations and Applications and VII Congress on Applied Mathematics", Salamanca, Spain (2001), and the 6th "France-Chile and Latinoamerican Conference on Applied Mathematics", at Santiago (2002).