Preface The present volume contains a sample of research work by young Mexican math- ematicians currently working abroad, on the occasion of the workshop “Matem´aticos Mexicanos ovenes en el Mundo”, which took place at CIMAT, in Guanajuato, Mexico, on August 22–24, 2012. The workshop had three main goals: fostering the collaboration and exchange of ideas among young Mexican mathematicians working abroad and their peers in Mexico exchanging experiences concerning studying and working overseas and designing strategies to strengthen links between mathemat- ical research institutions in Mexico and Mexican mathematicians around the world. The history of professional mathematics in Mexico is relatively recent and spans less than 75 years. The Instituto de Matem´ aticas of the Universidad Nacional Aut´ onoma de exico (UNAM) was created in 1942 in Mexico City and became the first center fully devoted to mathematical research in the country. The following year saw the foundation of the Sociedad Matem´ atica Mexicana (SMM) and the first issue of its research journal: the Bolet´ ın de la Sociedad Matem´ atica Mexicana. Nowadays, there are at least six mathematics research centers (with several units around the country) in addition to at least 19 schools and departments of math- ematics at public and private universities, according to a list maintained by the SMM. The development of mathematics as an active research discipline in Mexico has gone through several phases. Among these, one can identify a foundational period centered at the Instituto de Matem´ aticas at UNAM in the 1940’s and 1950’s which extended and deepened mathematical activity originated in the Facultad de Ciencias at UNAM. This period experienced an important influence from Solomon Lefschetz and culminated with the creation of the Centro de Investigaci´ on y Estu- dios Avanzados (CINVESTAV) and the Escuela Superior de ısica y Matem´aticas at the Instituto Polit´ ecnico Nacional (IPN) in 1961. A subsequent period of expansion was marked by the creation of the Centro de Investigaciones en Matem´ aticas Aplicadas, Sistemas y Servicios (CIMASS) at UNAM, in 1970, and the Universidad Aut´ onoma Metropolitana, in 1974. CIMASS eventually evolved into the actual Instituto de Investigaciones en Matem´ aticas Apli- cadas y en Sistemas (IIMAS), in 1976. In 1980 the Centro de Investigaci´ on en Mate- aticas (CIMAT) was founded and became one of the first public research centers outside Mexico City. In the last twenty years, the need for decentralization and the growth in some of the already established institutions have led to the creation of associated representations and units (e.g. Cuernavaca, Juriquilla and Oaxaca, ix
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