Rocky Mountain
Algebraic Combinatorics Seminar

The Algebraic Combinatorics Seminar is a joint venture of
Colorado State University, the University of Colorado at Denver and the University of Wyoming
The three university collaboration began in 1985, building on a CSU-UWyo seminar that dates back to the mid-70's, and it has been meeting discretely since then.

Organizing Members
A. Betten (CSU)
W. Cherowitzo (UCD)
R. Green (UCB)
S. Hobart (UWyo)
A. Hulpke (CSU)
G. Eric Moorhouse (UWyo)
S. Payne (UCD)
T. Penttila (CSU)
The seminar meets biweekly in Fort Collins, 4 - 6 on Fridays.
There are two talks given at each session.
This a joint seminar with regular participants from 5 universities in the region.
The participants usually dine at a local restaurant after the talks.
Please feel free to join us!
For more information contact: T. Penttila.
Participating Members
P. Vojtechovsky (DU)
J. Williford (UWyo)
N. Krier (CSU) (Emeritus)
In Memory

Next Meeting

Date: Friday 10 May 2013
Time: 4 - 6
Place: Weber 223 ( but refreshments at 330 in Weber 117)
Weber is on the oval just north of E wing of the Engineering building
Colorado State University

Optimally Topologically Transitive Orbits of the Bernoulli Shift Map

Francis Motta


Denseness is unrefined! So, in this talk, we will try to remedy the implication of this play on words by exploring a refinement of the notion of subset density for orbits of a discrete-time dynamical system on a topological space. In particular, for a fixed discrete-time dynamical system, $\Phi(x) : M \rightarrow M$ defined on a bounded metric space, we introduce a function $E: \{\gamma_x | x \in M\} \rightarrow \mathbb{R}\cup \{\infty\}$ on the orbits of $\Phi$, $\gamma_x := \{\Phi^t(x)| t \in \mathbb{N}\}$, and interpret $E(\gamma_x)$ as a measure of the orbit's \textit{approach} to density.

We first study a motivating example, the family of rigid rotations $R_\theta: [0,1) \rightarrow [0,1)$ ($\theta \in (0, 1))$ defined by $R_\theta(x) = (x + \theta) \mod 1$. We then discuss other discrete-time dynamical systems with dense orbits, including the Bernoulli shift map acting on sequences over a finite alphabet. This leads to a connection to (infinite) de Bruijn sequences. Finally, to compute approximations of $E(\gamma_x)$ for orbits of the Bernoulli shift map, we develop an efficient algorithm which determines a word in the set of all words of a fixed length over a finite alphabet whose distance to a distinguished subset is maximal.

A Different Perspective of Hyperovals in PG(2,2h)

Philip DeOrsey

University of Colorado Denver

A hyperoval in a finite projective plane of order q = 2h is a set of q + 2 points, no three of which are collinear. In 2006, Fisher and Schmidt presented a new way to view hyperovals using finite Fourier series. Motivated by their work, we are looking at hyperovals in PG(2,2h) from a perspective that is analogous to polar coordinates of the complex plane. We will discuss the results of Fisher and Schmidt, develop our polar perspective, and see how we can apply it to the Penttila-O’Keefe hyperoval in PG(2,32).

Schedule / Open Slots
Have a good summer!

Talks given in previous semesters

If you would like to added to our e-mail list, or would be interested in giving a talk, please contact T. Penttila.

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