Ross Willard, Pure Mathematics Department, University of Waterloo
"Introduction to the seminar"
This
is
the
first,
introductory
lecture
to
a
learning
seminar
on
discrete
homotopies
for
binary
reflexive
digraphs
and
their
application
to
finite
relational
structures.
In
this
lecture
I
will
briefly
overview
the
idea
of
homotopy,
state
Taylor's
theorem
(that
the
existence
of
continuous
operations
satisfying
nontrivial
laws
implies
the
fundamental
group
is
abelian),
and
indicate
how
we
plan
to
generalize
these
ideas
and
results
to
reflexive
digraphs
in
subsequent
weeks.
Finally,
I
hope
to
have
time
to
explain
the
motivation
for
why
one
might
want
to
do
this.