Title: Diagonal coefficients, graph invariants with the symmetries of Feynman integrals, and the proof of the c_2 completion conjecture
| Speaker: | Karen Yeats |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: In
a
scalar
field
theory
the
contribution
of
a
Feynman
diagram
to
the
beta
function
of
the
theory,
the
Feynman
period,
can
be
written
as
an
integral
in
terms
of
the
(dual)
Kirchhoff
polynomial
of
the
graph.
There
are
many
interesting
graph
theoretic
operations
under
which
this
integral
is
invariant,
and
we
can
better
understand
the
period
and
its
geometry
by
investigating
graph
invariants
with
these
same
symmetries.
Recently
Erik
Panzer
found
a
new
such
invariant
coming
from
a
particular
coefficient
of
the
Martin
polynomial.
Together
we
used
this
to
prove
an
over
10
year
old
conjecture
on
an
arithmetic
graph
invariant
known
as
the
c_2
invariant,
and
came
to
understand
that
diagonal
coefficients
of
Kirchhoff
polynomials
tie
together
many
of
the
known
graph
invariants
with
the
symmetries
of
Feynman
periods
and
unlock
previously
inaccessible
proofs.
Joint
work
with
Erik
Panzer