Geometric and Spectral Methods in Partial Differential Equations (16w5066)


(Johns Hopkins University)

(University of Illinois, Urbana-Champaign)

(Massachusetts Institute of Technology)



The Casa Matemática Oaxaca (CMO) will host the "Geometric and Spectral Methods in Partial Differential Equations" workshop from December 11th to December 16th, 2016.

Geometric analysis is, very roughly speaking, the study of geometry
using tools from the theory of functions and
especially from calculus (the ``analysis'' part of geometric
analysis). The topic is classical, dating
back in its nascent form at least to Euler in the early eighteenth
century. It has evolved to be one of the most important topics in
mathematics, and is furthermore central in the interplay between
mathematics and other fields, especially modern physics.
To name a few ``applications,'' one finds ideas from geometric
analysis in mathematical string theory, cosmology and general
relativity, the study of waves in all forms from graviational waves to water waves, to medical imaging and so many
other fields. It is thus at once extremely useful in the most
practical sense of the term and in the most abstract.

Our conference will bring together research experts in microlocal
analysis, a topic in geometric analysis related to the study
of partial differential equations, with experts in different fields in
the geometric analysis tent, particularly in dynamical systems,
spectral theory, and invariant theory. Microlocal analysis has been
shown to be an essential tool in the most central questions in current
geometric analysis, as it provides a means for studying differential
equations in settings which are singular (picture a cone with a sharp
point or a piece of paper with a creased fold) or non-compact
(infinite planes or other shapes which have no border but continue on
to infinity.) As in previous conferences of this type, we expect to
have a fruitful interplay between microlocal analysts and other
geometers, as each even the nominally separate topics we mention have
deep and growing connections.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.