CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Joseph McCollum, Univ. at Albany 

Time:          Wednesday, November 30, at 4:30pm       

Place:         Earth Sciences 152A, Univ. at Albany 

Title:         Random Walks on the Dihedral Group $D_{2p}$



Abstract:

This talk will center around the details needed to prove the following theorem.

Let $\epsilon > 0$ be given.
Suppose $k$ is a fixed integer which is at least 3 and $p$ is a prime greater
than or equal to 3.
If we pick uniformly at random $K$, which is a $k$-subset from
$G=D_{2p}$ with at least one rotation and one flip, then for some values $N$
and $\gamma>0$,
\[
E(\| P_{K}^{*m} - U \|) < \epsilon
\]
for $m = \lfloor{\gamma p^{2/(k-1)}}\rfloor $.  The expectation is over uniform
choices of $K$.

I will discuss the representation theory needed and give a quick proof of the
Upper Bound Lemma by Diaconis and Shahshahani
which is critical in finding the above bound.  


Refreshments at 4:15pm in ES 152.