Mathematics Archives

James Pascoe

Prof. James Pascoe is an assistant professor of mathematics at Drexel University, working in various areas of mathematics. He graduated from the University of California, San Diego, under the guidance of Prof. Jim Agler in 2015. Prof. Pascoe’s international collaborations span the globe and a variety of mathematical topics, all united by the theme of using functional analysis to explore the semantic meaning of mathematics through a variety of avatars of mathematics. His existing collaborations with junior mathematicians in India include those with Sujit Sakharam Damase, Chandan Pradhan, and Nitin Tomar.

For his Fulbright-Nehru project, Prof. Pascoe is working with researchers at the Indian Institute of Science, Bengaluru, with a focus on creating material links between the operator theory research communities in the United States and India. As part of the project, Prof. Pascoe, inspired by the great Hungarian mathematician Paul Erdős, is visiting various institutes in India and speaking on topics in modern operator theory, while also helping junior mathematicians in establishing their research programs and connections with the global community.

Nageswari Shanmugalingam

Prof. Nageswari Shanmugalingam is a distinguished research professor (STEMM) in mathematical sciences at the University of Cincinnati, Ohio. She obtained her PhD in mathematics in 1999 from the University of Michigan, Ann Arbor. Her research forms part of the foundation of the emergent field of analysis in metric measure spaces, and her current research interests include nonlinear potential theory, Dirichlet and Neumann boundary value problems in non-smooth setting, and non-local energies, with applications in geometry and quasi-symmetric mappings in non-smooth spaces, including fractals. She has more than 100 research publications in highly ranked mathematical research journals, and has coauthored a book (Cambridge University Press, 2015) on Newton-Sobolev mappings between metric spaces. She also has an extensive mathematical research network both in the U.S. and abroad. Her current research interests include the exploration of how Gromov hyperbolic geometry impacts the behavior of harmonic functions and how the dissipation of heat behaves.

In addition to conducting research in mathematics, Prof. Shanmugalingam is an educator, teaching courses at the undergraduate and graduate levels at the University of Cincinnati. She has also supervised the PhD research of six students and is currently supervising the dissertation research of three other students. She has also been a mentor to postdoctoral scholars.

The development of analysis in non-smooth spaces was motivated by the need to understand how quasi-symmetric classes of regular metric measure spaces share analytic behaviors. This development highlighted the crucial role played by geometric objects called “uniform domains”. On the other hand, recent developments in geometric group theory and fractal analysis indicate a need for discrete analogs of uniform domains. Prof. Shanmugalingam’s Fulbright-Nehru project is developing such analogs in collaboration with Prof. S. Ponnusamy at IIT Madras. The project is also introducing the field of non-smooth analysis to students by conducting a course on analysis in metric spaces.

John Lesieutre

Prof. John Lesieutre is an associate professor of mathematics at Pennsylvania State University, working in the field of algebraic geometry. He completed his education from Harvard and the Massachusetts Institute of Technology, after which he held a postdoctoral position at the University of Illinois at Chicago. His research focus is on the geometry of higher-dimensional algebraic varieties, which are sets of solutions to systems of polynomial equations in many variables. He is particularly interested in how symmetries of the solution sets of these systems can shed light on the geometry of the underlying systems of equations. He has published numerous articles in this field.

Prof. Lesieutre’s Fulbright-Nehru project has three major components: to initiate a new research collaboration on the algebraic aspects of K-stability with a researcher at the Indian Institute of Science (IISc); to teach an informal mini course for IISc graduate students on algebraic dynamics; and to continue his studies on algebraic dynamics.

Priyamvada Nambrath

Priya Nambrath is a doctoral candidate in the Department of South Asia Studies at the University of Pennsylvania. Her dissertation research focuses on the applied practice of mathematics and astronomy in the sociocultural life of medieval and pre-modern Kerala. More broadly, she is interested in the intellectual and scientific history of India with a focus on cultural encounters, archaic modernisms, patronage, and pedagogy. Language and literature, textual culture, and visual art constitute additional related areas of her focus. She is also interested in folk traditions of art and knowledge in South India, and the ocean-facing histories of the region.

Priya brings her previous training and work experience in science and mathematics to her current research interests in Indian scientific and educational history. She has taught university courses in Sanskrit and Malayalam language and literature and has published a translation of a Sanskrit play. She has also been a highly successful coach for competitive mathematics at the school level.

Under the Fulbright-Nehru Fellowship, Priya is researching the pedagogical approaches and cultural concerns that shaped the mathematical culture of South India in the pre-colonial and early colonial periods, with a focus on the Kerala school of Indian mathematics. She is conducting archival research on untranslated mathematical materials composed both in Sanskrit and in the vernacular languages. Priya hopes that her research will contribute to increasing awareness about a plurality of scientific traditions and pedagogical strategies which can be profitably utilized in modern classrooms.

Joseph Engmark

Joseph Engmark is pursuing his PhD in mathematical statistics from the Department of Mathematics at the University of Maryland. His research interests focus on design-based probability sample surveys. Since 2018, Joseph has been working in the Center for Statistical Research and Methodology at the U.S. Census Bureau. Prior to joining the bureau, he taught mathematics at secondary schools in Liberia and Malawi as a U.S. Peace Corps volunteer. Joseph has a broad interest in nature, cultural exchange, and the global community.

Under the Fulbright-Nehru fellowship, John is collaborating with researchers at the Indian Statistical Institute in Kolkata. The research project is focusing on capture-recapture methods, a survey sampling technique used to estimate totals in a finite population. These methods are widely used in practice, including in epidemiology, wildlife conservation, and official statistics, such as a census.