Shoma Sugimoto, "On the Feigin-Tipunin construction"

Video recording for "Tsinghua-Tokyo workshop on Calabi-Yau," January 15-19, Fuji Kenshujyo (富士研修所), Fujiyoshida, Japan.
[workshop webpage] indico.ipmu.jp...
[slides] Some slides are available from indico.ipmu.jp...
[abstract] Vertex algebra (VA) is a mathematical formulation of two-dimensional conformal field theory, and in the classical (rational) case, whose q-character gives a modular
form. Recently, due to the relationship between VAs and higher dimensional field theories,
the study of non-rational VAs has attracted a great deal of attention, but the examples
and representation theory are not well known. On the other hand, S.Gukov and collaborators have introduced a quantum invariant of 3-manifolds called homological blocks and
conjecture the existence of the corresponding non-rational VAs. In this talk, I will present
my results and plans for a special case of this conjecture. In particular, I will explain that
the homological block of a Seifert 3-manifold (corresponding to a false theta function) can
be recovered if we can repeatedly apply the procedure called Feigin-Tipunin construction
to a certain lattice VA (corresponding to a theta function).