Speaker
Adam Gutter, University of Waterloo
Abstract
Continuing
an
overview
of
Boris
Zilber's
textbook
Zariski
Geometries,
we
define
geometrically
motivated
conditions
on
a
topological
(model-theoretic)
structure,
building
towards
a
collection
of
conditions
which
will
guarantee
that
the
topological
structure
is
in
fact
isomorphic
to
a
smooth
algebraic
curve
over
an
algebraically
closed
field.
In
this
seminar,
we
define
the
notion
of
"good
dimension"
that
includes
as
an
example,
but
is
not
limited
to,
the
standard
dimension
of
an
algebraic
variety.
Using
this
notion,
we
define
a
class
of
model-theoretic
objects
known
as
Zariski
Structures,
which,
as
we
shall
see
later,
includes
geometric
objects
found
in
algebraic,
analytic,
and
differential
geometry.
Note:
This
seminar
corresponds
to
section
3.1
of
Zariski
Geometries.