Dr. Holder began a career in mathematics in 1998 after completing
Ph.D. studies at the University of Colorado at Denver under the
tutelage of Dr. Harvey Greenberg. His primary interest was in applied mathematics
and specifically in optimization, a field that
intersects numerous scientific disciplines. His current interests
lie in applying optimization techniques to problems in medicine,
biology, and economics. He holds a joint position in the department
of Radiation Oncology at the University of Texas Health Science
Center, and in close collaboration with his medical colleagues,
he is investigating how to improve patient care by optimizing radiotherapy
treatments. His initial work won the 2000 William Pierskalla award as
the best annual paper in Operations Research and Health Care.
His work in biology addresses a problem in population genetics called
the Pure Parsimony Problem. The basic question is what
is the minimum amount of diversity needed in the previous
generation to observe the current generation's genetic composition.
Computational efforts on this problem have not been successful,
and the mathematical attack of Dr. Holder's work provides
alternative methods in graph theory.
In economics, Dr. Holder extended a result of Paul Samuelson,
the 1970 Nobel Laureate in Economics. The original results is called
the Nonsubstitution theorem and has been credited with transitioning
economics from the neoclassic paradigm into modern economic theory.
Dr. Holder extended this famous result to a dynamic problem and
showed that the basic premise of the original result is maintained
asymptotically.
Dr. Holder has a strong background in undergraduate research, and
the work above has been accomplished largely through undergraduate
efforts. He has research collaborations with 15 undergraduates
spread over 7 articles and has directed numerous senior projects.
He also has participated in the Trinity NSFREU project for 5 summers.
Outside of mathematics, his hobbies include cycling, hiking, and auto
mechanics.
