Title:ÌýAsymptotics of the Euler characteristic of Kontsevich'sÌýcommutative graph complex
| Speaker: | Michael Borinsky |
| Affiliation: | ETH, Zurich |
| Location: | MC 5479 or contact Olya Mandelshtam for Zoom link |
Abstract:ÌýI
will
present
results
on
the
asymptotic
growth
rate
of
theÌýEuler
characteristic
of
Kontsevich's
commutative
graph
complex.
By
aÌýwork
of
Chan-Galatius-Payne,
these
results
imply
the
same
asymptoticÌýgrowth
rate
for
the
top-weight
Euler
characteristic
of
M_g,
the
moduliÌý
space
of
curves,
and
establish
the
existence
of
large
amounts
ofÌýunexplained
cohomology
in
this
space.
This
asymptotic
growth
rateÌý
follows
from
new
generating
functions
for
the
edge-alternating
sumÌýof
graphs
without
odd
automorphisms.
I
will
give
an
overview
on
thisÌý
interaction
between
topology
and
combinatorics
and
illustrate
theÌýcombinatorial
and
analytical
tools
that
were
needed
to
obtain
theseÌý
generating
functions.