Dear All,
There is a field called algebraic analysis (or microlocal analysis) originated in works by Sato and Kashiwara. They study differential equations combining complex analysis, sheaf theory, and D-modules. I do not know much about applications, but as far as I understood, these techniques allow to generalize Cauchy-Kowalevski theorem and play an important role in the computation of the index of a differential operator.
I think it might be interesting to invite somebody from this field to DART, maybe even ask to give couple of survey talks.
I found only one survey, but it is quite formal and does not include applications: https://arxiv.org/pdf/1206.1435v3.pdf (more theoretic)
Here are some people in the field http://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/ https://webusers.imj-prg.fr/~pierre.schapira/ http://docenti.math.unipd.it/dagnolo/coordinates.php?lan=0
Maybe you or members of PC know more about the subject and can give some recommendations.
Sincerely yours, Gleb