Changho
Han,
Department
of
Pure
Mathematics,
University
of
Waterloo
“Periods
I:
Elliptic
Curves
and
Hodge
Theory”
This
is
the
first
talk
in
the
series
of
two
talks
with
the
goal
of
introducing
a
method
of
parametrizing
isomorphism
classes
of
certain
varieties
using
analytic
techniques;
even
if
it’s
analytic,
this
particular
construction
(of
using
”periods”)
plays
key
roles
in
algebraic
side
of
algebraic
geometry
and
number
theory
as
well.
In
this
first
talk,
I
will
showcase
the
standard
construction
for
elliptic
curves,
as
a
differential
geometric
consequence
that
any
elliptic
curve
(as
a
complex
manifold)
is
a
quotient
of
complex
plane;
the
result
is
the
famous
quotient
of
the
upper
half-plane
by
SL(2,Z).
Then
I
will
re-interpret
this
construction
in
terms
of
cohomologies,
leading
to
the
Hodge
theory.
This
viewpoint
will
play
a
key
role
in
the
next
talk
when
we
look
at
K3
surfaces.
MC 5403
Zoom
information:
Meeting
ID:
817
1030
9714;
Passcode:
063438