Physics and Mathematics are two sciences that have always walked in parallel throughout history, and recent times are witnesses to how this interaction has become increasingly intense. On the one hand, for example, we see various attributions of the Fields Medal to mathematical works that solved problems from Physics. On the other hand, in Physics, Mathematics, its native language, is becoming an increasingly complex and sophisticated requirement, and new physical theories constantly require the development of new theories and fine mathematical tools.
This is the case of the need to formulate generalizations of non-Euclidean geometries for the space-time of General Relativity, the advent of string theories strongly based on geometry, topology, and algebra, the use of group theory, symmetries and topology in Physics of elementary particles, the relation between quantum groups (quasi-Hopf algebras, quasi-triangular) and statistical mechanics, etc.
The Patricio Letelier School on Mathematical Physics intends to contemplate and give more impetus to this deep symbiosis between Physics and Mathematics and intends to have a thematic character, even if some other specific topics, besides the predicted theme, are approached.
In its first version, held at UBU-ES, from 21 to 26 February 2016, the focus was mainly on the challenges that arise in the fields of Physics and Mathematics that emerge when trying to extend the formulation of the usual and (experimentally) successful Quantum Field Theory in Minkowski's space-time plane to the curved spaces. Such a process has generated unexpected effects in physics, such as the production of particles in an expanding universe and the thermodynamics of black holes. In mathematics, we were led to a deeper development of microlocal analysis, which imposed on us a strong relation to modern theories of bundles and categories to arrive at a rigorous formulation of relevant physical results in the subject. Problems of statistical physics and critical phenomena are also included in these large research programs.