:
In the context of integrable systems, the operator valued
Riemann-Hilbert
problems first appeared in the late 80s early 90s work of Nikita Slavnov
and his collaborators (the speaker included). It turns out that the
transition
to the operator valued Riemann-Hilbert setting manefistates the
transition from
free fermion to non free fermion exactly solvable quantum models. Very
recently,
the operator valued Riemann-Hilbert problems started to show up in the
problems
related to the integrable probability; notably, in the description of
the important
solutions of the KPZ equations. These are the works of I. Corwin, P.
Ghosal, T. Bothner, M. Cafasso, and S. Tarricone.
The principal goal of the talk is to remind the old, still unsolved
important
questions associated with the quantum operator valued Riemann-Hilbert
problems
and to highlight the new challenges emerged in the area due to its
involvement in the probabilistic applications.
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