Title: Eigenvalues of Hermitian matrices and Schubert calculus
| Speaker: | Alexander Yong |
| Affiliation: | University of Illinois, Urbana-Champaign |
| Room: | MC 5501 |
Abstract:
In
the
late
1990's
the
following
old
problem
was
solved:
how
does
the
condition
A+B=C
on
triples
of
Hermitian
matrices
constrain
their
eigenvalues?
Through
the
work
of
A.
Klyachko,
A.
Knutson-T.
Tao,
K.
Purbhoo-F.
Sottile
and
many
others,
a
connection
was
made
and
deepened
between
this
problem
and
classical
Schubert
calculus.
I
will
present
a
particular
extension,
relating
an
eigenvalue
problem
of
S.
Friedland
to
equivariant
Schubert
calculus.
This
is
joint
work
with
D.
Anderson
(Ohio
State
U.)
and
E.
Richmond
(Oklahoma
State
U).
The
proof
is
based
on
a
factorial
Schur
function
analogue
of
M.-P.
Schutzenberger's
theory
of
jeu
de
taquin,
developed
with
H.
Thomas
(U.
New
Brunswick).
In
current
work,
with
O.
Pechenik
(U.
Illinois),
we
give
a
generalization
to
obtain
a
Littlewood-Richardson
rule
for
the
equivariant
K-theory
of
Grassmannians.