The lecture focuses on finding the volume of polyhedra with constant
curvatures in arbitrary dimensions. For spherical polyhedra the volume is
encoded in Schl|\"afli functions. It turns out that Schl\"afli and
Lobachevsky
functions can be expressed as iterated integrals on the moduli space of
arrangements of hyperplanes.

In the case of the volume of simplices we show that
there exists a flat nilpotent connection on
the space of complex unidiagonal symmetric matrices
with logarithmic poles so that we obtain volume functions
as special horizontal sections.

Keywords:

Hyperplane Arrangements

Lecture #10701

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