Professor Jani Onninen received a three-year NSF grant, beginning June 2022, for his work on Energy-Minimal Principles in Geometric Function Theory. The project will explore energy-minimizing deformations and their applications to the study of non-linear elasticity—which examines how physical materials warp, bend, or are otherwise altered in response to stress—and will further develop analytic and geometric tools to address the mathematical challenges the resulting constraints present.

“In a very simplistic illustration, suppose a blacksmith is hammering a hot piece of iron or steel to create a new shape,” explains Onninen. “When to stop hammering? Every stroke creates an element of the energy-minimizing sequence of homeomorphisms. If the weak limit fails to be invertible, then it tells us when to stop hammering prior to the conditions favorable to the formation of cracks.”

The project will include research opportunities for graduate students over its three-year duration.

Professor Dan Coman was awarded a three-year NSF grant, beginning this July, for his project, Pluripotential Theory and Random Geometry on Compact Complex Manifolds. The project aims to advance knowledge and understanding in the areas of complex analysis (which studies functions depending on variables that are complex numbers), complex geometry and potential theory. These critical areas of study provide powerful tools for solving important problems in fields of pure and applied mathematics (such as image and signal processing) and physics.

“I will study spaces of sections of holomorphic line bundles and the asymptotics of the related Bergman kernel functions, for example, which in physics terms are related to the quantum mechanics of particles in magnetic field,” says Coman.

Coman will work together with colleagues at the University of Cologne, Germany, and Paul Sabatier University in Toulouse, France, for part of the research. And two current mathematics Ph.D. students, Melody Wolff and Jesse Hulse, will receive summer support under the grant.

Professor Lixin Shen was another recipient of a three-year NSF grant, for his Collaborative Research: Sparse Optimization for Machine Learning and Image/Signal Processing. There is a growing problem of overly large data sets in fields such as information technology, nanotechnology, biotechnology, civil infrastructure, environmental science, and an increasing demand for competent data processing models. Shen is leading an effort to develop a more computationally efficient approach to optimizing data.

“The success of the proposed research will provide the opportunity for many useful and interesting applications in mathematics, computer science, and medical communities,” explains Shen. “Our medical collaborator at MSKCC has shown great enthusiasm in developing our methods for medical image reconstruction when low radiation doses are used in emission computed tomography.”

The projects will heavily involve graduate students, helping to prepare them for the significant challenges that will continue to be posed by the big-data era. “Since the work has a strong relevance with industry, medical sciences and defense, the educational component of the proposed research will pave the way for job opportunities for students who take part,” Shen says.

Mathematics Professor Claudia Miller (left) and Associate Professor Stephan Wehrli (right) received an NSF grant to host the 3rd Upstate New York Topology Seminar on October 22 at Syracuse. The one-day, in-person conference brought together researchers from New York State and nearby regions, working in various areas of topology—primarily algebraic and low-dimensional—with the hopes of building a cohesive topology community in the region. Three distinguished young researchers, Francesco Lin (Columbia University), Allison N. Miller (Swarthmore), and Martina Rovelli (University of Massachusetts—Amherst) served as plenary speakers, and there were an additional 14 talks within parallel afternoon sessions.

The conference was the third installment of the UNYTS series, founded in 2017 by Miller and Wehrli, together with professors Inna Zakharevich of Cornell University and Adam Sikora of SUNY Buffalo.