Metroplex Algebraic Geometry, Algebra and Number
Theory (AGANT) Seminar, a joint venture of
UNT, UTA
and TCU
Date/Time/Room: Thursday (9/24/2009) at 5:30
pm in 304 Pickard Hall
Speaker: Dr.
Aaron Lauve, Visiting Assistant Professor, Department
of Mathematics, Texas A&M
University.
"Another Look at
Markoff's Work on Quadratic Forms"
Abstract: During his study of binary
quadratic forms a x^{2} + b x y + c y ^{2}
in the late 1800s, Markoff introduced necessary and sufficient
conditions on a reduced form f so that its minimum is less than 3.
He phrased his condition in terms of certain forbidden patterns of
a biinfinite word associated to f. From the Markoff condition one
gets a large class of binary words that we call Markoff words. In
this talk, we will see that the Markoff words are palindromes, and
indeed are the important central words from the theory of Sturmian
sequences. (This is joint work with Amy Glen and Franco Saliola.)
A map of UTA may be found at
http://www.uta.edu/maps/,
and directions to UTA are on that website. Note that PKH is the
triangular building in the centralcampus region of the map.
Select Pickard Hall from the building selector. PKH is next to the
``garage'' & is on Nedderman Dr between Planatarium Place (aka
College St) & West St. West St is oneway northbound between W
Mitchell St and 3rd St. Parking is available in the nearby (East
and SE of PKH) parking lots with a UTA permit (but many people
park there late on Fridays with no permit).
There are a few metered parking spots on the East side of Pickard
Hall on West St. Visitor (free), & metered, parking is
available by Davis Hall (marked DH in SW part of the submap). A
parking garage (expensive) is nextdoor to PKH (use West St to get
to it). Note that if heading south on Cooper, then no left turn is
allowed to Nedderman Dr. Note that PKH 304 is on the 3rd floor
of PKH; turn right out of elevator on 3rd floor.
