Log geometry gives a neat way of dealing with some degenerations in algebraic
geometry. For the purposes of our Introduction series, the main motivation comes from
the Gross-Siebert mirror symmetry program, where logarithmic stable maps play a
central and essential role.
In this talk, we will start with a refresher on schemes. A definition of some basic
notions in log geometry will follow, including log schemes, log differentials, and log
smoothness. We will illustrate these ideas in basic cases (to be defined in the talk)
such as the trivial log structure, a toric log scheme, a normal crossing divisor, a
logarithmic point, and a logarithmic line. If time permits, we will proceed to discuss
the Kato-Nakayama space -- a topological space associated to a log scheme that encodes
information about the log structure.
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