Maverick Science mag 2013-14

the hopes that such techniques might not only solve
equations of current interest, but also any equations of
the same type that might arise in physics in the future.”
Among Vancliff’s projects which could benefit research
in physics is one with Thomas Cassidy, professor
and math department chair at Bucknell University,
which focuses on generalizing the notion of Clifford algebra
and using geometry to motivate their proposed
generalization. Clifford algebras, which offer a direct
way to model geometric objects and their transformations,
have numerous applications in physics.
“Our work together involves a variation on classical
Clifford algebras. Clifford algebras have many applications
in theoretical physics, and we have been stretching
these ideas to encompass a broader family of algebraic
structures, with the hope of finding applications in
quantum physics,” Cassidy said. “Michaela is a remarkably
tenacious researcher. Mathematical research is
often characterized by sudden realizations or insights,
but those insights can only come after prolonged and
intense study. Michaela has the mathematical drive and
vision to delve into very abstract concepts and find hidden
connections.”
Vancliff is also working with UT Arlington associate
professor of math Dimitar Grantcharov, an expert in
representation theory, on a long-term project aimed at
describing a recently defined ring, called a graded skew
Clifford algebra, in terms of a Lie bracket and Poisson
geometry, and using that information to classify certain
modules of the ring. Vancliff and Cassidy were the first
ones to propose the idea of the graded skew Clifford algebra,
in 2010.
“Dr. Vancliff is a very talented mathematician and
she is highly dedicated to research, teaching and service,”
said Jianzhong Su, professor and chair of the math
department. “The field she works in is quite abstract,
even for other mathematicians, but this kind of mathematics
is reflective to some of the deeper insights in
modern physics. Dr. Vancliff is one of the leaders in this
research field, and the importance of her work is widely
recognized by the scientific community.”
A
n analytical mind was seemingly
hard-wired into Vancliff’s DNA.
She was born in England, northeast
of London in Essex County,
and her father was an electrical
engineer. He instilled in her a desire
to understand how things
work. Initially, she was interested
in physics, but in high school she was inspired by one of
her math teachers, who felt strongly that Vancliff should
pursue a mathematics degree. The teacher remained a
friend and mentor until his passing a few years ago.
“In hindsight, I believe I was interested in structural
patterns that make stuff work, more than in the physical
inner workings, and that interest translated into a desire
to understand the mathematics that explains how
stuff works,” she said. “From the entire cosmos down
to the tiniest flower petal, mathematics is behind the
scenes making it all work, and I wanted to understand
it all.”
After finishing secondary school, Vancliff enrolled at
the University of Warwick, in Coventry, England where
she earned a B.S. in Mathematics in 1986. Her degree
was in pure mathematics, but she also took courses in
quantum physics, special relativity and general relativity.
While at Warwick, one of the math faculty members
suggested that she pursue a graduate degree in the
United States, at the University of Washington.
“He was very familiar with the university and the city
of Seattle, and he felt that I would excel in that environment,”
Vancliff said. “Since I very much enjoyed living
in Seattle and being a student at the University of Washington,
I guess he was right.”
“Michaela is a remarkably
tenacious researcher. [She]
has the mathematical drive
and vision to delve into very
abstract concepts and find
hidden connections.”
– omas Cassidy
Bucknell University professor of mathematics
She taught high school math in London for a year
after graduating from Warwick, then moved to Seattle
and began work on a Ph.D. in mathematics with the intention
to focus on applied math. During her first year,
while taking a mandatory graduate algebra class, she
was introduced to the notion of a module over a ring.
“I immediately recognized it as a generalization of
the idea of matrices acting on a vector space, which is a
pervasive topic throughout all of the applied sciences,”
Vancliff said. “So a light bulb lit up in my brain, and I
fell in love with algebra.”
Her interests were mainly in physics applications, so
Vancliff was drawn to study modules over non-commutative
rings. At that time, the study of modules over
commutative rings had been ongoing for decades due
to the use of geometric techniques. In a bit of perfect
timing, Vancliff began her graduate studies just as a new
movement had started in the world of algebra that
pushed the study of non-commutative rings and their
modules via geometric techniques. This new subject became
known as non-commutative algebraic geometry.
“This was an entirely new subject, and I was fortunate
to enter it at its inception,” she said. “There were
many open problems ripe for the picking and many that
were accessible to junior researchers such as myself.
This meant that I was able to make groundbreaking
contributions to the subject while I was still a student,
simply because the subject was so new. I found it to be
very exciting.”
Vancliff says that she was fortunate that her Ph.D.
advisor at the University of Washington, S.P. Smith,
took his responsibilities very seriously.
“Not only does he have a rare gift for being able to
explain mathematics and its intricate beauty, but he also
devoted time to teaching me how to write research publications
and funded my participation at conferences
and workshops,” Vancliff said. “He actively encouraged
me to network and interact with famous mathematicians,
and those opportunities proved to be invaluable
to me throughout my career.”
Vancliff earned her Ph.D. in 1993, and then worked
for two years as a visiting assistant professor at the University
of Southern California in Los Angeles. From
there, she moved to Belgium and worked for a year as a
researcher at the University of Antwerp, before spending
two years at the University of Oregon in Eugene. In
1997, Vancliff had a conversation with a colleague in
Oregon which led to a significant career decision. The
colleague had family living in Fort Worth and was familiar
with the North Texas region.
“He felt very strongly that I would be happy working
at UT Arlington and living in the DFW area, so he encouraged
me to apply to UT Arlington,” Vancliff said. “I
investigated UT Arlington online and found a vibrant,
growing university.”
When she interviewed in 1998, she found that the
department was strong in applied mathematics and less
so in algebra, which Vancliff took as a “positive challenge”.
She joined the faculty as an assistant professor
starting that fall.
“The department has changed much in the past 15
years, and its research has grown in strength, with many
of the current faculty earning research grants,” she said.
Her own research has been continuously funded since
her arrival.
V
ancliff is working with her graduate
students on several projects.
She and third-year doctoral student
Richard Chandler are looking
at the point schemes and line
schemes of a family of algebras
and trying to understand the algebras'
underlying structure.
Chandler first met Vancliff when he was an undergraduate
in her Abstract Algebra class in 2010. He earned a
B.A. in Mathematics with teaching certification in May
2011 and entered the Ph.D. program that fall. He wants
to go into academia after earning his doctoral degree.
“Dr. Vancliff is an amazing mentor,” Chandler said.
“She has very high standards for all of her students, but
they are always reasonable. She doesn’t expect perfection,
but she does expect that you put 100 percent into
all aspects of your work.”
Padmini Veerapen studied under Vancliff and
earned a Ph.D. in May 2013. She’s now an assistant professor
of math at Tennessee Technological University in
Cookeville, Tenn.
“Dr. Vancliff emphasized a level of detail and thoroughness
during my years under her supervision that is
allowing me now to successfully handle all my responsibilities
as a faculty member,” Veerapen said.
In addition to her research and teaching, Vancliff is
the organizer of the long-running DFW Algebraic
Geometry, Algebra and Number Theory (AGANT) seminar
series, which brings together researchers and students
from academia and industry in the Metroplex and
beyond and features national and international speakers.
She also created the department’s Graduate Forum,
which helps junior Ph.D. students by letting them talk
with faculty mentors and senior doctoral students.
“It is very fulfilling and satisfying to share my knowledge
with my students and see them enjoy the material
as much as I do,” Vancliff said. “When they see the connections
that I see and share with me their delight in
finding new connections, I can see how much they have
grown mathematically, and that is a joy to witness. It is
particularly exciting to see them continue a research
path after graduation, especially in academia where they
can continue this sharing of knowledge with the next
generation of students.”
Vancliff says that helping and sharing her knowledge
with others, working as part of a team, and using the
technical expertise she has acquired to solve problems
are all rewarding aspects of her job as a researcher and
educator.
“I very much enjoy that my work at UTA entails all
these components, both individually and in combination,”
she said. “I also find that my success at earning
research grants renews my energy, not only in the research
arena, but in all aspects of my job. I consider myself
very fortunate to be able to work in my chosen
career, and in the supportive environment of UTA.” n
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