Log geometry and the Riemann-Hilbert correspondence
Arthur Ogus
2.10pm-4.00 pm February 22
939 Evans Hall, Berkeley
ABSTRACT: The development of log geometry proper began about fifteen years ago
with the goal of understanding
the number-theoretic properties of varieties with bad reduction. The
underlying philosophy, however,
is very geometric and inspired by classical techniques used in the study
of compactifications of algebraic varieties.
In the first half of my talk I will try to explain a little of the
history and philosophy of log geometry. For the second half I will
discuss the "log Riemann-Hilbert correspondence," which gives a
topological classification of differential equations with
log poles. It turns out that the holomorphic germs of such connections
are classified by equivariant Higgs bundles on a cone associated with
the log structure. This construction can be globalized on a new
topological space
that gives a a compactification of the underlying variety that doesn't
change its local homotopy type.
LECTURE NOTES ARE AVAILABLE:
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