Professor John Ryan of the Department of Mathematical Sciences in the J. William Fulbright College of Arts and Sciences recently gave an invited talk at the conference "Complex Function Theory, its Generalizations and Applications" at the Instituto Nazionale di Alta Matematica in the Department of Mathematics, Universita di Roma "La Sapienza," in Rome, Italy.

The conference took place Sept. 12-16, 2016 and Ryan spoke on "Conformally Invariant Higher Spin Knapp-Stein Convolution Type Operators and Associated Differential Operators." The Instituto Nazionale di Alta Matematica is Italy's most prestigious math conference center.

Ryan said his talk explored various types of conformally invariant convolution type operators for higher spin settings, in the context of introducing uncountable infinite such operators and giving a class of conformally invariant differential operators acting as inverses to these operators.

Ryan also used the Cayley transform to carry over these results from euclidean space to the sphere, and collaborated with his doctoral students Chao Ding and Raymond Walter on this work. Other participants at the conference came from across the U.S., Mexico, Israel, Belgium, France, Germany and Serbia.

"I was very pleased to be invited to present at this conference," Ryan said. "I specialize in Clifford analysis, with a particular interest in the links between Dirac type operators and conformal structures so this was a wonderful opportunity to share these passions."

Additionally, Ryan recently had a conference held in his honor, titled "A Colloquium on Honor of John Ryan's 60th Birthday."

Ryan was the second scholar to ever receive a Higher Doctorate of Science from University of York, U.K., conferred in 2008. He was also a co-investigator on the first NSF grant given to fund a conference on Clifford analysis in 2014, and received the prestigious von Humboldt Fellowship from the Technical University of Freiberg, Germany in 1995.

He is also frequently called upon by prominent universities to serve on Ph.D. examining committees, most recently at the University of Newcastle in New South Wales, Australia in 2014 and previously for mathematics at the University of Montreal, Canada; Monash University, Australia; the Technical University of Freiberg, Germany; the University of Macau, Macau; and the University of Maryland, College Park.

About the Department of Mathematical Sciences: The Department of Mathematical Sciences offers degrees with focuses on applied math, pure math and statistics. Courses prepare students for careers in secondary education, actuarial science and industry and graduate school. Students will receive a broad, interdisciplinary education, highlighting the utility and value of mathematics in many careers and disciplines. 

About the J. William Fulbright College of Arts and Sciences: The J. William Fulbright College of Arts and Sciences is the largest and most academically diverse unit on campus with 19 departments and 43 academic programs and research centers. The college provides the core curriculum for all University of Arkansas students and is named for J. William Fulbright, former university president and longtime U.S. senator.