Dr. Rosen has published round 50 research papers and has written two books - "A Classical Introduction to Modern Number Theory" (co-authored with Kenneth Ireland) and "Number Theory in Function Fields", both in Springer's GTM Series. He has also co-edited with David Goss and David Hayes "The Arithmetic of Function Fields" published by Walter DeGruyter.

He has supervised 20 PhD theses, including one by a certain Josh Holden.

In 1999, Dr. Rosen won the Chauvenet Prize of the Mathematical Asociation of America for his article "Neils Henric Abel and Equations of the Fifth Degree". In 2001 he was awarded the Phillip Bray Award of Brown University for excellence in teaching within the physical sciences.

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 NSF-REU project for 5 summers.

Outside of mathematics, his hobbies include cycling, hiking, and auto mechanics.

Cancer is treated with three basic modalities: surgical, which physically removes a cancerous growth; drug therapy, which targets all fast proliferating cells; and radiotherapy, which locally irradiates tissues. Radiotherapy treatments are delivered by focusing beams of ionizing radiation on a patient so that the aggregate energy is highest over a targeted region. The goal is to deliver enough radiation to kill cancerous cells but not enough to harm surrounding structures. The design process has many facets, all of which have been aided by recent mathematical and computational results. We will discuss several of these recent advances.

A new treatment paradigm called photodynamic therapy is loosely a combination of drug therapy and radiotherapy. The idea is to develop a drug, called a photosensitizer, that when excited by an infrared light destroys tissue. There are two obstacles. First, it is difficult to chemically design a photosensitizer with a heightened affinity for cancerous cells, and hence, the drug is equally collected in all tissues. Second, the optical properties of infrared light are not favorable to targeting deep tissues. Combined, these two concerns mean that it is challenging to treat growths within the anatomy. We will show that even if the infrared light was focused optimally, the current drugs do not allow the treatment of tumors more than a few millimeters from the surface. This means that improved chemical properties are needed to make this a viable treatment. Moreover, we estimate the amount of drug improvement needed to successfully treat tumors several centimeters into the anatomy.