Women's Seminar Fall 2008 Schedule
Meeting: Friday 12pm in 148 Henry Administration Building
- September 2: Organization meeting
- September 19: Sylvia Carlisle
Title: Model theory of
$\R$-trees, again.
Abstract: An $\R$-tree is
a metric space such that between any two points there is a unique arc, and
that arc is a geodesic segment. Continuous logic is an extension of
classical first-order logic which is set up to deal with
metric structures. The continuous theory of $\R$-trees has a model
companion. I will give a very quick introduction to continuous logic and
model theory for metric structures. Then I will very generally explain
what it means to have a model companion and how to characterize the one
for the theory of $\R$-trees. I hope to make liberal use of pictures,
hand waiving and analogies.
- September 26: Valerie
Peterson
Title: Robots and cube complexes: a geo-group-ological
perspective
Abstract: A variety of settings in manufacturing,
robotics, biology, chemistry and other areas
suggest a need to coordinate moving agents in some optimal fashion. In
this talk,
I'll introduce a cube complex that records independent moves in many
'reconfigurable systems' and helps determine optimal paths for motion (or
at least
helps us keep our robots from colliding). I will also present some
interesting
geometric, topological and group theoretic properties of these complexes.
This
talk has been designed with undergraduates in mind but I hope it will be
entertaining for those from a wide variety of backgrounds.
- October 10: Lale Ozkahya
Title: Cycles in Hypercube
Abstract: $Q_n$ denotes the n-dimensional hypercube,
which is the graph on vertex-set $\{0,1\}^n$ and edge-set assigned between
pairs differing in exactly one coordinate. Given graphs P and Q, the
generalized Turan number ex(Q,P) denotes the maximum number of edges of a
P-free subgraph of Q.
Erd\"os (1984) conjectured that $ex(Q_n,C_4) = (1/2+o(1))e(Q_n)$, where
$e(Q_n)$ is the number of edges in $Q_n$. We consider the case when P is
a cycle of length 4k+2 for positive integer k and Q is $Q_n$. This is
joint work with Zolt\'an F\"uredi.
- October 24: Supawadee Prugsapitak
Title: The Tarry-Escott problem over Gaussian
integers
Abstract: The Tarry-Escott problem asks to find two
different sets of integers $A = \{a_1,\dots,a_n\}$ and $B =
\{b_1,\dots,b_n\}$ so that $\sum a_i^j = \sum b_i^j$ for $1 \le j \le k$.
We call $k$ the degree of a solution. In any solution $n \ge k+1$; if
$n=k+1$, the solution is called ideal. In this talk, we discuss the
Tarry-Escott problem over the Gaussian integers and characterize ideal
solutions of degree 2. If we have time, we will discuss about how to
obtain the higher degree solutions over Gaussian integers.
- November 7: Jeehyeon Seo
Title:Bi-Lipschitz embedding on doubling space
Abstract:I will talk about doubling space that can be
embedded Bi-Lipschitzly in some Euclidean space.
- November 21: Veena Paliwal
Title:Moving boundary value problem with noise
Abstract:We will consider effect of noise on moving
boundary value problem. In particular, we will look at heat equation with
2 parameter noise.
- December 5: Mercredi
Chasman
Title: Vibrations of a beam under variable tension
Abstract: We'll look at the vibrational modes and
frequencies of an unconstrained beam and see how they change as functions
of a tension parameter. When this parameter is positive, the beam is under
tension; when it is negative, the beam is under compression and has both
vibrating and buckling modes.