4 Plus 1, Raised to a Higher Power

The American Mathematical Society (AMS) selected four of the five full professors in the Polytechnic Institute of New York University (NYU-Poly) Mathematics Department to its inaugural class of Fellows of the AMS. An NYU-Poly professor emeritus was also selected.

The Fellows of the AMS designation recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics. Among the goals of the program are to create an enlarged class of mathematicians recognized by their peers as distinguished for their contributions to the profession and to honor excellence.

The NYU-Poly professors chosen for the honor are Department Head Erwin Lutwak, Deane Yang, Yisong Yang and Gaoyong Zhang, as well as Professor Emeritus Lesley M. Sibner.

“NYU-Poly’s faculty and students take special pride in the scholarship of Professors Lutwak, Yang, Yang, Zhang and Sibner,” said NYU-Poly Acting President and Provost Katepalli R. Sreenivasan. “By being named 2013 Fellows of AMS, their peers formally recognize them as accomplished mathematicians. This honor demonstrates that exceptional scholarship can be fostered in small departments such as the Mathematics Department at NYU-Poly. I congratulate them on this honor.”

Three of the professors – Lutwak, Deane Yang and Zhang – are widely recognized for their collaborative scholarship on convex geometric analysis and its connections to electrical engineering. They regularly publish peer-reviewed research in not only mathematical journals but also electrical engineering ones – which is rare for pure mathematicians. Reconstructing the shapes of three-dimensional CAT-scan images is just one of the ultimate applications of convex geometric analysis. 

Yisong Yang's areas of research are partial differential equations and mathematical physics. His contributions include construction of vortices in supersymmetric field theory, which are essential for the quark confinement mechanism, derivation of universal growth laws relating energy and topology for knots arising in a quantum field theory model in arbitrary dimensions, and existence theory for cosmic strings, which are responsible for matter accretion and galaxy formation in the early universe.

Sibner works on nonlinear partial differential equations and gauge field theory. She constructed the original version of a nonlinear, non-regular Hodge theory. She has many results about removing point singularities in Yang-Mills connections. She showed the existence of non-minimal solutions to the Yang-Mills equations over the four sphere. More recently, she has shown the existence of singular connections on the four sphere with holonomy. She recently demonstrated the existence of hyperbolic Higgs monopoles with arbitrary mass at infinity, which may have connections to the illusive Higgs boson. She also organized scientific meetings as associate secretary of AMS.

The AMS is the world’s largest and most influential society dedicated to mathematical research, scholarship and education.