Thursday, September 6, 2001
| Title |
An Anti-Ramsey Theorem on Posets |
| Speaker |
Professor Greg McColm |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Abstract
One of the generalizations of Ramsey Theory has been to posets. It is known
that for any finite poset P, there is a finite poset Q such
that any 2-coloring of the nodes of Q yields a monochromatic copy of
P. We will explore some of the results surrounding this fact, including
the fact that for any trees S, T, and any 2-coloring of the
Cartesian product S × T into red nodes and blue nodes,
there is either a red copy of S or a blue copy of T. Then we
will find a pair of finite posets P, Q, and a 2-coloring of
P×Q admitting no red copy of P nor a blue
copy of Q.
Thursday, September 13, 2001
| Title |
An Anti-Ramsey Theorem on Posets, II |
| Speaker |
Professor Greg McColm |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Thursday, September 20, 2001
| Title |
Solutions of Bethe Ansatz Equations in Some Physics Models |
| Speaker |
Professor Mourad Ismail |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Abstract
The Bethe Asatz equations are nonlinear algebraic equations satisfied by the
eigenvalues of a physical system. Stieltjes solved these equations for the Coulomb
gas model. This work is also connected to earlier work of Heine who counted
the number of polynomial solutions to second order differential equations with
polynomial coefficients. Q-analogues of these results will be described
and I will show the connection with Bethe Ansatz equations for the XXX and XXZ
models. In doing so one needs to develop a new theory of singuarities of second
order equations in the Askey-Wilson operators.
Thursday, September 27, 2001
| Title |
Difference Equations, Orthogonal Polynomails, and Rogers-Ramanujan
Identities |
| Speaker |
Professor Mourad Ismail |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Abstract
We show how the Rogers-Ramanujan identities follow from studying difference
equations motivated by orthogonal polynomials. In particular this explains and
gives infinite families of generalizations of a list of Rogers-Ramanujan identities
developed in the 1960's by L. J. Slater, who claimed it was a complete list.
Thursday, October 4, 2001
| Title |
A Non-Monotonic Propositional Logic |
| Speaker |
Professor Richard Stark |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Thursday, October 11, 2001
| Title |
A Non-Monotonic Propositional Logic, II |
| Speaker |
Professor Richard Stark |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Thursday, October 18, 2001
| Title |
A Non-Monotonic Propositional Logic, III |
| Speaker |
Professor Richard Stark |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Thursday, October 25, 2001
| Title |
Graph Homomorphisms and Graph Automorphisms |
| Speaker |
Professor Brian Curtin |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
Abstract
Let G and H denote finite simple graphs. An automorphism
of H is a permutation of its vertices which maps adjacent vertices to
adjacent vertices (and nonadjacent vertices to nonadjacent vertices). Let
Aut(H) denote the full group of automorphisms of H. A
homomorphism of G into H is a map from the vertex set of
G to that of H which maps the endpoints of edges of
G to the endpoints of edges of H. We discuss the use of
graph homomorphisms in determining the automorphisms of a graph.
More precisely, we do the following. Fix a natural number n, and let
p and q denote n-tuple of vertices of
H. We show that if p and q belong to distinct
orbits under the action of Aut(H) then there is a graph G
and an n-tuple r of vertices of G such that the
number of homomorphisms from G into H maping r to
p element-wise differs from the number of homomorphisms from
G into H mapping r to q element-wise.
To prove this result we shall use some classical results on polynomial invariants
of finite groups.
Thursday, November 1, 2001
| Subject |
Ph.D. Program Review Planning Session |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |
We will discuss what we will say to the Ph.D. committee next week.
Thursday, November 14, 2001
| Title |
Graph Homomorphisms and Graph Automorphisms, Part II |
| Speaker |
Professor Brian Curtin |
| Time |
2:00-3:00 p.m. |
| Place |
LIF 267 |