[Blueboard] Dissertation Defense

cka at mathsci.math.admu.edu.ph cka at mathsci.math.admu.edu.ph
Tue Dec 7 08:51:09 PHT 2010

Mr. Beaunonie R. Gozo, Jr.
Ph.D. Math candidate

will defend his dissertation entitled "On Non-Perfect Colorings of  
Tilings with Associated Color Groups of Index at most 4"
on December 13, (Monday) at 4:30 p.m. in SEC-A304.


In this work, a framework will be presented that will allow for the  
construction and enumeration of non-perfect colorings of symmetrical  
tilings.  If G is the symmetry group of an uncolored tiling, a  
coloring of the tiling is non-perfect if its associated color is a  
proper subgroup of G.  The method will facilitate the construction of  
non-perfect colorings of a wider class of tilings where the stabilizer  
of a tile in G is non-trivial.  The paper will also discuss results on  
how to identify and construct non-perfect colorings arising from the  
method with associated color groups of index at most 4.

Non-perfect colorings of tilings will be presented that emerge from  
the hyperbolic semi-regular tiling 8-10-16 and selected 2-isohedral  
tilings in the Euclidean plane. Semi-regular tilings and isohedral,  
2-isohedral tilings are of importance in crystallography to represent  
and differentiate various chemical, physical and geometrical aspects  
of crystalline structures.  The discovery of quasicrystals generated  
more interest in the study of colored tilings particularly those that  
exhibit non-periodic symmetries such as 5-, 8- and 12-fold rotations.

Panel of examinees:
Dr. Reginaldo M. Marcelo, Mathematics Department, AdMU
Dr. Job A. Nable, Mathematics Department, AdMU
Dr. Rene P. Felix, Mathematics Department, UP-Diliman
Dr. Teofina A. Rapanut, UP-Baguio

Dissertation Adviser:
Dr. Ma. Louise Antonette N. De las Penas, Mathematics Department, AdMU

The dissertation defense is open to the public.

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