*During this meeting, which internationally highlights the excellence of mathematical achievement in the Americas, Manuel del Pino delivered the only plenary lecture on partial differential equations.*

From July 24 to 28 in Montreal, about two thousand mathematicians gathered for a new version of the Mathematical Congress of the Americas (MCA), which seeks to unite the best of modern mathematics in the United States and Canada with Latin America.

In this scenario, the academic of the Department of Mathematics of the University of Chile and researcher CAPDE, Manuel del Pino, gave the plenary talk entitled “Formation of singularity and bubbles in non-linear diffusions”. Research that shows results obtained together with researchers CAPDE, Juan Davila and Monica Musso, in collaboration with Juncheng Wei (UBC, Canada), on the theme of formation of singularities in finite and infinite times in some problems of evolution in equations in partial derivatives .

“In the opening part of the talk, I tried to emphasize the importance of this subject in mathematics. The analysis of singularity formation in PDE is important by itself and by its applications and links with other areas of mathematics. For example, one of the so-called “Millennium Problems” in mathematics, of the great open questions in mathematics, corresponds to a question of this type, and studying these things led to the resolution of the only problem of the Millennium so far solved, The Poincaré Conjecture. In this context, the talk was aimed at a general mathematical audience, not necessarily specialists in PDE”.

In addition to the plenary talks, more than 70 special sessions were held at this meeting of mathematicians from the Americas. A remarkable effort, which demonstrates the vitality of this discipline in America, and the pertinence of having a meeting of this type every four years.University of Chile scholar and CAPDE member Claudio Muñoz, invited to the session of dispersive equations, gave the talk “Decay of small perturbations in equations of 1D scalar field”, research in collaboration with Michal Kowalczyk of the University of Chile and Yvan Martel (U. Versailles, France).

Finally, the CAPDE researcher, Juan Dávila dictated a subplenary talk and also a talk as a guest to a special session. On this occasion, the academic of the Department of Mathematics of the University of Chile, gave the talk called, “Singularities in finite time for the flow of harmonic maps in 2D with values in the sphere”.

As explained by Manuel del Pino, the conference as such, is a very interesting experience because of the variety of mathematics that brings together. “It’s a very wide audience and participating in this event was a very interesting experience. I think it is very valuable to bring together a large group of mathematicians from the Americas. It is probably the only one of its kind. “Along with this, del Pino emphasized that “there is a mathematical critical mass sufficiently broad in Latin America so that such a type of encounter is significant, it makes us feel a unity within the extended continent of Latin America with the US and Canada, and in that sense, I believe that as an event of exchange and approchement, between these groups is enriching as mutual knowledge”.