Kutztown
University of Pennsylvania
Department of
Mathematics
Spotlight Faculty member
December 2011
Dr. Kunio Mistuma
earned his B.S. (summa cum laude) in mathematics at Nihon University, Tokyo, Japan; his M.S. in
mathematics, West Virginia University; and his Ph.D. in mathematics (Semigroups) at the Pennsylvania State University.
During his middle school years in Tokyo, a
friend of his and he had intense rivalry in mathematics, primarily in terms of
who scored higher on exams. They were and are good friends. One day, around the
time they were studying the Quadratic Formula for the first time, his friend
said to Dr. Mitsuma that he had found out there are
actually formulas for the general 3rd-degree and 4th-degree
polynomials. He went on to say that, in the 17th century, the work
of a mere 20-year-old French mathematician led to the discovery that there is
no formula for the general 5th degree polynomial. Both of them were
fascinated by the non-existence of such a formula, and they wanted to learn
more! This is how Dr. Mitsuma set his eyes on
mathematics in his future.
Galois theory, as is commonly referred to, studies the correlations
among certain algebraic structures. The theory has had profound influence in
all branches of mathematics and other areas of science. By design, it concerns
only finite groups and so-called pairing finite fields. During his sophomore
year in college in Tokyo, as he studied Galois Theory, he found a
passage in a textbook that said there are ways to extend the original results
to infinite groups. Like the discussion with his friend in his teens, the
thought of infinite Galois theory fascinated him. So,
that's what he decided to study at Penn State because they had leading
mathematicians in that field.
Infinite Galois theory brings in topology to make a bridge from finite to
infinite groups. His research concentrates on topological semigroups,
which have less structural constraints than general topological groups. Because
of the leaner footprint, topological semigroups
exhibit simple yet beautiful behaviours.
As Dr. M. teaches number theory and abstract algebra at
Kutztown, his hope is that some students will be fascinated by the algebraic
structures that they study, and that they will eventually realize how much
mathematics we need to study in order to fully understand, for example, why two
rational numbers are the "same."
October 2011
Dr. Perry Y. C. Lee earned his B.Sc. in Mathematics and BSc. in
Engineering as well as earning his M.Sc. in Applied Mathematics at Queen's
University in Kingston, Ontario, Canada.
He earned his Ph.D. Ph.D.
in Mechanical Engineering from the University of Waterloo in thermal radiation
heat transfer.
Dr. Lee has
been with the Department of Mathematics at Kutztown University of Pennsylvania
since Fall 2005.
His
research interests are in the area of numerical heat transfer.
Prior to
his current appointment as a professor at Kutztown University, he was a Senior
Nuclear Engineer where one of his primary responsibilities was conducting
nuclear safety analysis work for Ontario Power Generation, a company that operates
nuclear power plants for the safe generation of electricity.
During his
ten year career in industry, he has applied mathematics extensively in the area
of environmental, mechanical, and nuclear engineering.
He is also a licensed Professional Engineer (P.Eng.) of Ontario, Canada.
November 2010
Dr. Yun "Amy" Lu earned her B.S. in applied
mathematics from
Dr. Lu’s research interests are in the application of
model theory to combinatorial structures, especially the classification of the reducts on random graphs and random bipartite graphs. Model
theory is an important branch of mathematical logic, studying mathematical
structures by considering first-order sentences which are true of those
structures and the sets which are definable in those structures by first-order
formulas. It has numerous applications to theory to algebra, especially ordered
fields and differential fields. She is also interested in bioinformatics,
analysis of algorithm etc. Bioinformatics is the integration of mathematics,
statistics, informatics, physics and biological sciences for the analysis of
biochemical, genetic and other related biological data.
September 2010
Dr.
Ju Zhou earned her B.S. in Mathematics and
M.S. in Operation Research from Zhengzhou University in China. She earned her Ph.D. in Mathematics and M.S.
in Statistics from West Virginia University in August of 2008. Before
coming to Kutztown University of Pennsylvania as a tenure track faculty member
in the fall of 2009, she worked as an instructor at Penn State
Worthington-Scranton in PA for one year and as a tenure-track Assistant
Professor for one year at Bridgewater State College in Massachusetts.
Dr Zhou's research interests lie in the field of graph theory and matroid theory. Her research interests include Induced Matching Problems, Cycles Related Problems and Group Connectivity Problems. In her thesis for her Master’s degree in Operation Research, she successfully characterized a series of induced matching extendable graphs. Her doctoral dissertation and current research focus on cycles in graph theory and matroids. In graph theory, researches about cycles, especially Hamiltonian cycles have been going on for a long time. One of the most important conjectures about Hamiltonian Cycles is the famous Thomassen’s conjecture: every 4-connected claw-free graph is Hamiltonian. One of her research interests is to work towards this conjecture. There are quite a lot of results in graph theory about the properties of cycles. The other research interest of hers is to extend all these cycles and edges related results in graph theory to a broader filed, matroid theory. She also does research in group connectivity.
May 2010
Dr. Jennifer Gorman is a
graduate of Ramapo College. She earned her Ph.D. from Lehigh University in
August of 2007. Before coming to Kutztown University as
a tenure track faculty member in the Fall of 2009 she held a position as
Assistant Professor for two years at Gannon University in Erie, PA.
Dr Gorman's research interests lie in the field of
graph theory. In the most basic definition graph theory looks at the properties
that arise when we place a bunch of dots on a piece of paper and connect some
or all of them with lines. Graph theory is one of the younger areas of
mathematics research. One of the reasons Dr. Gorman
especially likes graph theory is because many of the
problems can be looked at from the stance of solving a puzzle. This is one of
the reasons she feels it is an especially good area for undergraduate research.
She is able to state the problem in such a way that students are able to dive
right into working on the problem, even if they have never had a class on graph
theory.
Specifically Dr. Gorman
works in an area of Graph Theory concerned with finding Hamiltonian Cycles. Her
thesis and current research look at a variant of the Travelling Salesperson
Problem called the Nested Travelling Salesperson Problem on threshold graphs.
The problem can be thought of as the following ``puzzle'': A salesman has a
list of n cities that are all connected by roads that he wishes to visit, along
with some other information on the way the roads are connected. He is never
allowed to travel on a road more than once or backtrack on a road he has
already visited. If the roads have costs of 1, 2, and 3 how should the salesman
travel to maximize the number of 1 roads he travels on
and then maximize the number of 2 roads and finally fill in with 3 roads.
She encourages any student who likes to think about
and solve puzzles to come and talk to her and find out more about this exciting
area of Mathematics.
April 2010
Dr. Eric Landquist is a graduate of Virginia Tech
and earned his Ph.D. in Mathematics from the University of Illinois in 2009.
After a couple short post-doctoral stints at Carl von Ossietzky Universitaet in Oldenburg, Germany and the University of
Calgary in Calgary, Alberta, Canada, Dr. Landquist
joined the Kutztown University Department of Mathematics as a tenure-track
Assistant Professor in the fall of 2009.
Dr. Landquist's research interests include Cryptography
and Computational Algebraic Number Theory. His doctoral dissertation and
current research center on cubic function fields,
which are cubic extensions of Fq (x): the field of fractions of the polynomial ring over
the finite field Fq: Some cryptographic protocols
in use today apply such groups based on elliptic curves, curves of the the form
y2 = ax3 + bx + c, and the (quadratic) function fields determined by
them. Cubic function fields, on the other hand, are too slow and insecure to be
used for cryptographic applications. However, there are several open
theoretical and computational questions concerning cubic function fields.
In particular, Dr.
Landquist studies the arithmetic of ideals of the ring of integers associated
with these fields, along with the arithmetic of the infrastructure of these
fields. (The infrastructure of a field is a commutative, but non-associative
group-like structure found within the ideal class group of the ring of
integers.) He uses this arithmetic to compute the orders of special groups,
such as the aforementioned ideal class group, related to function
fields. In addition, not much is known about infrastructures, since they are
not groups; this opens up a huge box full of questions waiting for
answers.
Last updated: 17 Apr. 2010
© 2007 - 2010, DOMKUP
Kutztown University of Pennsylvania, Department of Mathematics, Dr. Paul
Ache, Chair
Any problems, suggestions, or comments please contact Dr. Padraig
McLoughlin, 265 Lytle Hall: mcloughl{at}kutztown.edu