The three research directions of this workshop can be summarized as follows:
Mathematics: At genus zero, there is a well-understood framework of single-valued periods, supported through the so-called single-valued map, that especially helps to identify the single-valued analogues of multiple zeta values and multiple polylogarithms. At genus one, similar constructions are being established, for example finding single-valued analogues of iterated Eisenstein integrals or elliptic multiple zeta values.
String amplitudes: Single-valued periods arise naturally in the low-energy expansions of closed-string amplitudes both in flat space and in AdS curvature corrections. In this way, closed-string amplitudes can be seen as the single-valued image of open-string amplitudes. While at tree-level single-valued multiple zeta values appear in the closed-string amplitude, at one-loop so-called modular graph forms play an important role as single-valued periods.
Feynman integrals: In order to have more structured approaches to solving and understanding complicated Feynman integrals, certain techniques for single-valued periods can be applied.
While single valuedness strictly speaking only appears in very specific limits of Feynman integrals, the function space of Feynman integrals in dimensional regularization offers a laboratory of objects where a single valued completion could be found, in particular coming from the framework of twisted (co)homology theory.
