INDIANAPOLIS -- Roland Roeder, Ph.D., a mathematician from the School of Science at Indiana University-Purdue University Indianapolis (IUPUI), will receive $460,000 over the next five years from the National Science Foundation's Division of Mathematical Sciences to support his research in pure math and the training of students from the graduate to high school levels.
The Faculty Early Career Development award is the NSF's most prestigious award in support of junior faculty. It is given to individuals who "exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research."
The award will support Roeder's research on dynamics in several complex variables, an area of pure mathematics focusing on the theoretical underpinnings of systems that change with time.
"Systems that change with time appear at the core of nearly all scientific endeavors, including biology, chemistry, physics and the social sciences," he noted. "Given the current state of a system, can one predict its future state? How does this evolution of the state of the system depend on the parameters of the system?
"Many such dynamical systems are far too complicated for a rigorous study, so one often resorts to simpler models, which are hoped to indicate the types of behavior that one should expect experimentally. One venue for such simpler models is the iteration of holomorphic maps, the topic of my NSF-supported research."
According to Roeder, insights obtained from complex dynamics have already provided a deeper understanding of real-world problems in a variety of fields including the study of magnetic materials and astrophysics.
In addition to supporting Roeder's research, his CAREER grant will provide research training including tuition and living expenses for one or two doctoral students he will supervise over the next five years. The funding will also enable Roeder and the Department of Mathematical Sciences to hold two workshops for graduate mathematics students from universities throughout the United States. Each workshop will provide opportunities for students to make presentations and will bring top researchers to IUPUI to speak and interact with the students.
Among the novel aspects of Roeder's NSF-supported work is his mentorship of extremely talented high school students on research projects and the continuation, along with Jeffrey Watt, Ph.D., associate dean for student affairs and outreach in the School of Science, of their co-organization of the IUPUI High School Math Contest, a highly respected competition that has been held for 17 years and recently expanded to include schools from throughout Indiana.
"You can't do anything properly without logical reasoning and math is the art of logical reasoning," said Roeder, who credits the awakening of his interest in the field as a young teen in Southern California to a local college faculty mentor who worked with motivated high school students. "A major goal of what we are doing here at IUPUI is providing students I like to call Super Stars -- talented high school students who work extremely hard -- with mentoring and an opportunity to learn advanced math, conduct original research and publish the results. Remarkably, they perform at the level of first-year graduate students."
Roeder credits Pavel Bleher, Ph.D., Chancellor's Professor of Mathematical Sciences at IUPUI, for getting him involved in leading high school students on research projects. The two mathematicians have had an impressive track record of mentoring exceptional students including a three-person team that won first place in the prestigious 2010 Siemens Competition in Math, Science and Technology and an individual student who was a 2013 Intel Science Talent Search Finalist. Roeder's previous NSF grant provided funding for him to mentor these students.
Yushi Homma, the Intel talent-search finalist and a recent Carmel (Ind.) High School graduate, will attend Stanford University in fall 2014 where he plans to major in math or possibly computer science. The 18-year-old Homma has been meeting with Roeder weekly for almost two years to work on a problem involving polynomials whose coefficients are random variables (a concept not typically covered until upper level college math). While maintaining a full high school course load, on average Homma had been spending about eight hours a week on this math problem, although he admits to ramping up to 20 hours a week in the month before the Intel competition deadline.
"I like math," said Yushi Homma, the son of a lawyer and a homemaker. "I began participating in national math competitions in sixth grade but by the time I was 13 or 14 I realized that I preferred research because it was both a cumulative assessment of my math knowledge and a way to expand that knowledge. Working with Drs. Bleher and Roeder has helped launch me into the field."
Under Roeder's and Bleher's continued tutelage, Homma is spending his last summer before college preparing a manuscript for submission to a peer-reviewed professional journal, a task that his mentors say very few high school students can accomplish, although this is the third time their mentees have a paper of this level. Interestingly, two of the other papers were written by the team that was successful in the Siemens competition -- a team that included Yushi Homma's older brother Youkow, currently a math major at Yale University.
"Roland Roeder is the first math department faculty member at IUPUI to receive this award from the National Science Foundation. Seven current School of Science faculty members now hold this prestigious award, an impressive number that underscores the high quality of the School's faculty and its commitment to education, research and community outreach," said Simon Rhodes, Ph.D., dean of the school.
Other NSF Career Award recipients in the School of Science are faculty members Yogesh Joglekar (physics); Gavriil Tsechpenakis, Murat Dundar and Mohammad Al Hasan (computer and information science); Gregory Druschel (earth sciences) and Haibo Ge (chemistry and chemical biology).
The School of Science at IUPUI is committed to excellence in teaching, research and service in the biological, physical, behavioral and mathematical sciences. The school is dedicated to being a leading resource for interdisciplinary research and science education in support of Indiana's effort to expand and diversify its economy.