Among the most exciting developments in PDEs in the last few decades is the interplay
between CR (Cauchy-Riemann) geometry, as a branch of Complex Analysis, and the general
theory of locally integrable PDE systems, going back to the classical work of Hörmander, H.
Lewy, Nirenberg, Treves. The main goal of this project is to push this interplay further. We will
study the solvability (exactness) of the tangential Cauchy-Riemann complex on classes of
generic submanifolds of the complex space, and investigate regularity problems for CR-maps
between submanifolds. We will study local, semi-global and global solvability, and for CR-maps
their analytic and Gevrey regularity. The novelty of the approach is to bring techniques from the
general theory of locally integrable structures. We as well plan extending regularity phenomena
from the CR-case to more general structures. We will put together the close but still
complimentary expertise of the Czech team, specializing on CR-geometry, and the Sao Paulo
team, specializing on the general theory of locally integrable structures.

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